M src/hash/rescue/arch/x86_64_avx2.rs → src/hash/rescue/arch/x86_64_avx2.rs

@@ -5,36 +5,41 @@ // https://github.com/0xPolygonZero/plonky2/blob/main/plonky2/src/hash/arch/x86_64/poseidon_goldilocks_avx2_bmi2.rs
 
 // Preliminary notes:
 // 1. AVX does not support addition with carry but 128-bit (2-word) addition can be easily emulated.
-//    The method recognizes that for a + b overflowed iff (a + b) < a: i. res_lo = a_lo + b_lo ii.
-//    carry_mask = res_lo < a_lo iii. res_hi = a_hi + b_hi - carry_mask
+//    The method recognizes that for a + b overflowed iff (a + b) < a:
+//    1. res_lo = a_lo + b_lo
+//    2. carry_mask = res_lo < a_lo
+//    3. res_hi = a_hi + b_hi - carry_mask
 //
-//    Notice that carry_mask is subtracted, not added.
-//
-//    This is because AVX comparison instructions return -1 (all bits 1) for true and 0 for false.
+//    Notice that carry_mask is subtracted, not added. This is because AVX comparison instructions
+//    return -1 (all bits 1) for true and 0 for false.
 //
 // 2. AVX does not have unsigned 64-bit comparisons. Those can be emulated with signed comparisons
 //    by recognizing that a <u b iff a + (1 << 63) <s b + (1 << 63), where the addition wraps around
 //    and the comparisons are unsigned and signed respectively. The shift function adds/subtracts 1
-//    << 63 to enable this trick. Addition with carry example: i. a_lo_s = shift(a_lo) ii. res_lo_s
-//    = a_lo_s + b_lo iii. carry_mask = res_lo_s <s a_lo_s iv. res_lo = shift(res_lo_s) v. res_hi =
-//    a_hi + b_hi - carry_mask
+//    << 63 to enable this trick. Addition with carry example:
+//    1. a_lo_s = shift(a_lo)
+//    2. res_lo_s = a_lo_s + b_lo
+//    3. carry_mask = res_lo_s <s a_lo_s
+//    4. res_lo = shift(res_lo_s)
+//    5. res_hi = a_hi + b_hi - carry_mask
 //
 //    The suffix _s denotes a value that has been shifted by 1 << 63. The result of addition
 //    is shifted if exactly one of the operands is shifted, as is the case on
-//    line ii. Line iii. performs a signed comparison res_lo_s <s a_lo_s on shifted values to
-//    emulate unsigned comparison res_lo <u a_lo on unshifted values. Finally, line iv. reverses the
+//    line 2. Line 3. performs a signed comparison res_lo_s <s a_lo_s on shifted values to
+//    emulate unsigned comparison res_lo <u a_lo on unshifted values. Finally, line 4. reverses the
 //    shift so the result can be returned.
 //
-//    When performing a chain of calculations, we can often
-//    save instructions by letting the shift propagate through and only undoing it when necessary.
+//    When performing a chain of calculations, we can often save instructions by letting
+//    the shift propagate through and only undoing it when necessary.
 //    For example, to compute the addition of three two-word (128-bit) numbers we can do:
-//    i. a_lo_s = shift(a_lo)
-//    ii. tmp_lo_s = a_lo_s + b_lo
-//    iii. tmp_carry_mask = tmp_lo_s <s a_lo_s
-//    iv. tmp_hi = a_hi + b_hi - tmp_carry_mask
-//    v. res_lo_s = tmp_lo_s + c_lo vi. res_carry_mask = res_lo_s <s tmp_lo_s
-//    vii. res_lo = shift(res_lo_s)
-//    viii. res_hi = tmp_hi + c_hi - res_carry_mask
+//    1. a_lo_s = shift(a_lo)
+//    2. tmp_lo_s = a_lo_s + b_lo
+//    3. tmp_carry_mask = tmp_lo_s <s a_lo_s
+//    4. tmp_hi = a_hi + b_hi - tmp_carry_mask
+//    5. res_lo_s = tmp_lo_s + c_lo vi. res_carry_mask = res_lo_s <s tmp_lo_s
+//    6. res_carry_mask = res_lo_s <s tmp_lo_s
+//    7. res_lo = shift(res_lo_s)
+//    8. res_hi = tmp_hi + c_hi - res_carry_mask
 //
 //    Notice that the above 3-value addition still only requires two calls to shift, just like our
 //    2-value addition.