Fix markdown in NTT documentation (risc0#181)

* Docstring VerifyRoundInfo

* add some comments

* add long comment

* bazelisk rustfmt

* typo

* another typo

* explain bit_reverse

* delete copy paste error

* add newlines for readability

* remove asterisks

* comment on fold_eval

* escape brackets for markdown

* update more escapes

* fix ntt

* Update fri.rs

risc0/zkp/rust/src/core/ntt.rs

@@ -138,39 +138,60 @@ butterfly!(1, 0);
 /// The result of this computation is a discrete Fourier transform, but with
 /// changed indices. This is described [here](https://en.wikipedia.org/wiki/Cooley%E2%80%93Tukey_FFT_algorithm#Data_reordering,_bit_reversal,_and_in-place_algorithms)
 /// The output of rev_butterfly(io, n) at index i is the sum over k from 0 to
-/// 2^n-1 of io[k] * ROU_REV[n]^(k*i'), where i' is i bit-reversed as an n-bit
+/// 2^n-1 of io\[k\] ROU_REV\[n\]^(k i'), where i' is i bit-reversed as an n-bit
 /// number.
 ///
 /// As an example, we'll work through a trace of the rev_butterfly algorithm
 /// with n = 3 on a list of length 8. Let w = ROU_REV[3] be the eighth root of
 /// unity. We start with
-///   [a0, a1, a2, a3, a4, a5, a6, a7]
+///
+///   \[a0, a1, a2, a3, a4, a5, a6, a7\]
+///
 /// After the loop, before the first round of recursive calls, we have
+///
 ///   [a0+a4, a1+a5,     a2+a6,         a3+a7,
-///    a0-a4, a1*w-a5*w, a2*w^2-a6*w^2, a3*w^3-a7*w^3]
+///
+///    a0-a4, a1w-a5w, a2w^2-a6w^2, a3w^3-a7w^3]
+///
 /// After first round of recursive calls, we have
+///
 ///   [a0+a4+a2+a6,         a1+a5+a3+a7,
-///    a0+a4-a2-a6,         a1*w^2+a5*w^2-a3*w^2-a7*w^2,
-///    a0-a4+a2*w^2-a6*w^2, a1*w-a5*w+a3*w^3-a7*w^3,
-///    a0-a4-a2*w^2+a6*w^2, a1*w^3-a5*w^3-a3*w^5+a7*w^5]
+///
+///    a0+a4-a2-a6,         a1w^2+a5w^2-a3w^2-a7w^2,
+///
+///    a0-a4+a2w^2-a6w^2, a1w-a5w+a3w^3-a7w^3,
+///
+///    a0-a4-a2w^2+a6w^2, a1w^3-a5w^3-a3w^5+a7w^5]
+///
 /// And after the second round of recursive calls, we have
+///
 ///   [a0+a4+a2+a6+a1+a5+a3+a7,
+///
 ///    a0+a4+a2+a6-a1-a5-a3-a7,
-///    a0+a4-a2-a6+a1*w^2+a5*w^2-a3*w^2-a7*w^2,
-///    a0+a4-a2-a6-a1*w^2-a5*w^2+a3*w^2+a7*w^2,
-///    a0-a4+a2*w^2-a6*w^2+a1*w-a5*w+a3*w^3-a7*w^3,
-///    a0-a4+a2*w^2-a6*w^2-a1*w+a5*w-a3*w^3+a7*w^3,
-///    a0-a4-a2*w^2+a6*w^2+a1*w^3-a5*w^3+a3*w^5-a7*w^5,
-///    a0-a4-a2*w^2+a6*w^2-a1*w^3+a5*w^3-a3*w^5+a7*w^5]
+///
+///    a0+a4-a2-a6+a1w^2+a5w^2-a3w^2-a7w^2,
+///
+///    a0+a4-a2-a6-a1w^2-a5w^2+a3w^2+a7w^2,
+///
+///    a0-a4+a2w^2-a6w^2+a1w-a5w+a3w^3-a7w^3,
+///
+///    a0-a4+a2w^2-a6w^2-a1w+a5w-a3w^3+a7w^3,
+///
+///    a0-a4-a2w^2+a6w^2+a1w^3-a5w^3+a3w^5-a7w^5,
+///
+///    a0-a4-a2w^2+a6w^2-a1w^3+a5w^3-a3w^5+a7w^5]
+///
 /// Rewriting this, we get
-///   [sum_k ak w^0,
+///
+///   \[sum_k ak w^0,
 ///    sum_k ak w^4k,
 ///    sum_k ak w^2k,
 ///    sum_k ak w^6k,
 ///    sum_k ak w^1k,
 ///    sum_k ak w^5k,
 ///    sum_k ak w^3k,
-///    sum_k ak w^7k]
+///    sum_k ak w^7k\]
+///
 /// The exponent multiplicands in the sum arise from reversing the indices as
 /// three-bit numbers. For example, 3 is 011 in binary, which reversed is 110,
 /// which is 6. So i' in the exponent of the index-3 value is 6.