@@ -58,15 +58,15 @@ unconstrained fn __batch_invert_impl<let N: u32>(mut x: [F; N]) -> [F; N] {
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unconstrained fn __compute_fracs (z : F , ys : [F ; FIELDS_PER_BLOB ]) -> [F ; FIELDS_PER_BLOB ] {
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let mut denoms : [F ; FIELDS_PER_BLOB ] = [BigNum ::new (); FIELDS_PER_BLOB ];
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for i in 0 ..FIELDS_PER_BLOB {
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- denoms [i ] = z .__add (NEGATIVE_ROOTS [i ]); // (z - ω ^i)
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+ denoms [i ] = z .__add (NEGATIVE_ROOTS [i ]); // (z - omega ^i)
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}
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- let inv_denoms = __batch_invert_impl (denoms ); // 1 / (z - ω ^i), for all i
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+ let inv_denoms = __batch_invert_impl (denoms ); // 1 / (z - omega ^i), for all i
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let mut fracs : [F ; FIELDS_PER_BLOB ] = [BigNum ::new (); FIELDS_PER_BLOB ];
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for i in 0 ..FIELDS_PER_BLOB {
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- let inv_denom = inv_denoms [i ]; // 1 / (z - ω ^i)
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+ let inv_denom = inv_denoms [i ]; // 1 / (z - omega ^i)
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- fracs [i ] = ys [i ].__mul (inv_denom ); // y_i / (z - ω ^i)
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+ fracs [i ] = ys [i ].__mul (inv_denom ); // y_i / (z - omega ^i)
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}
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fracs
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}
@@ -260,9 +260,9 @@ fn main(blob: [F; FIELDS_PER_BLOB], kzg_commitment: [Field; 2]) -> pub (Field, F
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/**
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* ___d-1
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- * z^d - 1 \ ω ^i
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+ * z^d - 1 \ omega ^i
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* p(z) = --------- . / y_i . ---------
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- * d /____ z - ω ^i
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+ * d /____ z - omega ^i
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* i=0
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*
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* p(z) = factor . sum( y_i . num / denom )
@@ -271,7 +271,7 @@ fn main(blob: [F; FIELDS_PER_BLOB], kzg_commitment: [Field; 2]) -> pub (Field, F
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* where d = 4096
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*
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* Precompute:
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- * - The d roots of unity ω ^i (plus maybe their negatives for z - ω ^i computations).
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+ * - The d roots of unity omega ^i (plus maybe their negatives for z - omega ^i computations).
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* - (1 / d)
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*
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* @param z
@@ -342,48 +342,48 @@ fn barycentric_evaluate_blob_at_z(z: F, ys: [F; FIELDS_PER_BLOB]) -> F {
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let mut sum : F = BigNum ::new ();
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// Making a call to this function causes a "stack too deep" error, so I've put the body of that function here, instead:
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- // let fracs = __compute_fracs(z, ys); // { y_i / (z - ω ^i) }
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+ // let fracs = __compute_fracs(z, ys); // { y_i / (z - omega ^i) }
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// Note: it's more efficient (saving 30k constraints) to compute:
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// ___d-1
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// \ / y_i \
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- // / | --------- | . ω ^i
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- // /____ \ z - ω ^i /
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+ // / | --------- | . omega ^i
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+ // /____ \ z - omega ^i /
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// i=0
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// ^^^^^^^^^
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// frac
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//
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// ... than to compute:
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//
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// ___d-1
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- // \ / ω ^i \
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+ // \ / omega ^i \
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// / y_i . | --------- |
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- // /____ \ z - ω ^i /
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+ // /____ \ z - omega ^i /
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// i=0
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//
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- // perhaps because all the ω ^i terms are constant witnesses?
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+ // perhaps because all the omega ^i terms are constant witnesses?
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//*****************************************************************
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// This section is only needed because `__compute_fracs` isn't working (stack too deep error).
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- let mut fracs : [F ; FIELDS_PER_BLOB ] = [BigNum ::new (); FIELDS_PER_BLOB ]; // y_i / (z - ω ^i), for all i
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+ let mut fracs : [F ; FIELDS_PER_BLOB ] = [BigNum ::new (); FIELDS_PER_BLOB ]; // y_i / (z - omega ^i), for all i
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let mut denoms = [BigNum ::new (); FIELDS_PER_BLOB ];
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for i in 0 ..FIELDS_PER_BLOB {
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- denoms [i ] = z .__add (NEGATIVE_ROOTS [i ]); // (z - ω ^i)
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+ denoms [i ] = z .__add (NEGATIVE_ROOTS [i ]); // (z - omega ^i)
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}
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// If you're seeing a `bug` warning for this line, I think it's fine.
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// Ideally, we'd be using `__compute_fracs`, anyway, but we're getting a "stack too deep" error.
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- let inv_denoms = __batch_invert_impl (denoms ); // 1 / (z - ω ^i), for all i
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+ let inv_denoms = __batch_invert_impl (denoms ); // 1 / (z - omega ^i), for all i
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for i in 0 ..FIELDS_PER_BLOB {
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let num = ys [i ];
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- let inv_denom = inv_denoms [i ]; // 1 / (z - ω ^i)
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+ let inv_denom = inv_denoms [i ]; // 1 / (z - omega ^i)
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- let frac = num .__mul (inv_denom ); // y_i * (1 / (z - ω ^i))
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+ let frac = num .__mul (inv_denom ); // y_i * (1 / (z - omega ^i))
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- fracs [i ] = frac ; // y_i / (z - ω ^i)
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+ fracs [i ] = frac ; // y_i / (z - omega ^i)
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std:: as_witness (fracs [i ].limbs [0 ]);
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std:: as_witness (fracs [i ].limbs [1 ]);
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std:: as_witness (fracs [i ].limbs [2 ]);
@@ -414,9 +414,9 @@ fn barycentric_evaluate_blob_at_z(z: F, ys: [F; FIELDS_PER_BLOB]) -> F {
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// Seeking:
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// ___d-1
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- // \ ω ^i
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+ // \ omega ^i
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// sum = / y_i . ---------
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- // /____ z - ω ^i
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+ // /____ z - omega ^i
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// i=0
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let NUM_PARTIAL_SUMS = FIELDS_PER_BLOB / 8 ;
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for i in 0 ..NUM_PARTIAL_SUMS {
@@ -426,26 +426,26 @@ fn barycentric_evaluate_blob_at_z(z: F, ys: [F; FIELDS_PER_BLOB]) -> F {
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// Seeking:
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// ___i*8 + 7
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- // \ ω ^k
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+ // \ omega ^k
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// partial_sum = / y_k . ---------
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- // /____ z - ω ^k
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+ // /____ z - omega ^k
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// k=i*8 + 0
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for j in 0 ..8 {
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let k = i * 8 + j ;
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- lhs [j ] = ROOTS [k ]; // ω ^k
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- rhs [j ] = fracs [k ]; // y_k / (z - ω ^k)
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+ lhs [j ] = ROOTS [k ]; // omega ^k
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+ rhs [j ] = fracs [k ]; // y_k / (z - omega ^k)
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std:: as_witness (lhs [j ].limbs [0 ]);
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std:: as_witness (lhs [j ].limbs [1 ]);
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std:: as_witness (lhs [j ].limbs [2 ]);
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std:: as_witness (rhs [j ].limbs [0 ]);
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std:: as_witness (rhs [j ].limbs [1 ]);
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std:: as_witness (rhs [j ].limbs [2 ]);
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- // y_k * ( ω ^k / (z - ω ^k) )
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+ // y_k * ( omega ^k / (z - omega ^k) )
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let summand = ROOTS [k ].__mul (fracs [k ]);
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- // partial_sum + ( y_k * ( ω ^k / (z - ω ^k) ) -> partial_sum
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+ // partial_sum + ( y_k * ( omega ^k / (z - omega ^k) ) -> partial_sum
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partial_sum = partial_sum .__add (summand );
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std:: as_witness (partial_sum .limbs [0 ]);
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std:: as_witness (partial_sum .limbs [1 ]);
@@ -454,19 +454,19 @@ fn barycentric_evaluate_blob_at_z(z: F, ys: [F; FIELDS_PER_BLOB]) -> F {
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// Seeking:
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// ___i*8 - 1 ___i*8 + 7
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- // \ ω ^i \ / y_k \
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- // sum_out = / y_i . --------- + / ω ^k . | --------- |
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- // /____ z - ω ^i /____ \ z - ω ^k /
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+ // \ omega ^i \ / y_k \
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+ // sum_out = / y_i . --------- + / omega ^k . | --------- |
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+ // /____ z - omega ^i /____ \ z - omega ^k /
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// 0 k = i*8
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// ^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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// sum partial_sum
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//
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// ... that is:
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//
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// ___i*8 - 1 ___ 7
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- // \ ω ^i \
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+ // \ omega ^i \
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// sum_out = / y_i . --------- + / lhs[j] . rhs[j]
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- // /____ z - ω ^i /____
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+ // /____ z - omega ^i /____
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// 0 j = 0
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// ^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^
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// sum partial_sum
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