Progress towards making zkp field-agnostic (risc0#238)

* Define "field::Elem" and "field::ExtElem" types
* Add test_roots_of_unity and test_field_ops test utils to run basic tests on fields (It sounds like kalen and @tzerell will be working more on tests and documentation)
* Rename baby bear field (15*2^27) from {Fp, Fp4} to field::baby_bear::{Elem, ExtElem}; Fp and Fp4 are now aliases
* Change a bunch of Fp and Fp4 calls to use trait items.
* Remove Fp::invalid, so we don't have to keep this complication for all our fields. (and we weren't using it in rust anyways)

risc0/zkp/rust/benches/ntt.rs

@@ -14,7 +14,8 @@
 
 use criterion::{criterion_group, criterion_main, BenchmarkId, Criterion};
 use rand::thread_rng;
-use risc0_zkp::core::{fp::Fp, ntt::interpolate_ntt, Random};
+use risc0_zkp::core::{fp::Fp, ntt::interpolate_ntt};
+use risc0_zkp::field::Elem;
 
 pub fn ntt(c: &mut Criterion) {
     let mut group = c.benchmark_group("interpolate_ntt");

risc0/zkp/rust/src/adapter.rs

@@ -18,6 +18,7 @@ use anyhow::{bail, Result};
 
 use crate::{
     core::{fp::Fp, fp4::Fp4},
+    field::Elem,
     taps::TapSet,
     INV_RATE,
 };
@@ -55,7 +56,7 @@ impl CircuitStepContext {
 
     pub fn _set(&self, base: &mut [Fp], value: Fp, offset: usize, _loc: &str) {
         let reg = &mut base[offset * self.size + self.cycle];
-        assert!(*reg == Fp::invalid() || *reg == Fp::new(0) || *reg == value);
+        assert!(*reg == Fp::new(0) || *reg == value);
         *reg = value;
     }
 
@@ -322,7 +323,7 @@ impl CircuitStep {
             CircuitStep::Set(base, value, offset, _loc) => {
                 let value = stack[*value];
                 let reg = &mut args[*base][offset * ctx.size + ctx.cycle];
-                assert!(*reg == Fp::invalid() || *reg == Fp::new(0) || *reg == value);
+                assert!(*reg == Fp::ZERO || *reg == value);
                 *reg = value;
             }
             CircuitStep::GetGlobal(base, offset, _loc) => {