chore: remove decompose function (#92)

Author: jialinli98

src/_string_tools/slice_packed_field.nr

@@ -594,37 +594,11 @@ fn divmod_31(numerator: u16) -> (u16, u16) {
     (quotient, remainder)
 }
 
-/**
- * @brief converts a 16 bit value into 16 fake bools (Field elements that are 0 or 1)
- **/
-unconstrained fn decompose(val: Field) -> [Field; 16] {
-    let mut r: [Field; 16] = [0; 16];
-
-    let mut it = val as u32;
-    for i in 0..16 {
-        r[i] = (it & 1) as Field;
-        it >>= 1;
-    }
-    r
-}
-
 // 5 gates?
-pub fn get_last_limb_path<let OutputFields: u32>(last_limb_index: Field) -> [Field; OutputFields] {
+pub fn get_last_limb_path<let OutputFields: u32>(last_limb_index: Field) -> [u1; OutputFields] {
     // TODO we offset by 1 explain why (0 byte length produces 0 - 1 which = invalid array index. we just add 1 and increase array length by 1 to compensate)
     let path = LAST_LIMB_PATH[cast_num_to_u32(last_limb_index + 1)]; // 2
-    // Safety: check the comments below
-    let path_valid_bits = unsafe { decompose(path) };
-    let mut path_valid_sum: Field = 0;
-    let mut path_valid_output: [Field; OutputFields] = [0; OutputFields];
-    for i in 0..OutputFields {
-        // we check that the path valid bits are binary
-        assert(path_valid_bits[i] * path_valid_bits[i] - path_valid_bits[i] == 0);
-        path_valid_sum += (path_valid_bits[i] * (1 << i as u8) as Field);
-        path_valid_output[i] = path_valid_bits[i];
-    }
-    // we check that the path valid bits sum to the path
-    assert(path_valid_sum == path);
-    path_valid_output
+    path.to_le_bits::<OutputFields>()
 }
 
 /**
@@ -728,13 +702,13 @@ pub fn slice_fields<let InputFields: u32, let OutputFields: u32>(
     // 1, 70.5
     let index_of_output_limb: Field = (num_bytes_div_31 as Field - num_bytes_mod_31_is_0 as Field);
     // 5, 75.5
-    let path_valid_output: [Field; OutputFields] = get_last_limb_path(index_of_output_limb);
+    let path_valid_output: [u1; OutputFields] = get_last_limb_path(index_of_output_limb);
 
     // 2, 77.5
     let tail_shift = BYTE_SHIFT[cast_num_to_u32(num_unused_bytes_in_start_limb)];
 
     // 51, 128.5
-    let mut result = [0; OutputFields];
+    let mut result: [Field; OutputFields] = [0; OutputFields];
     let mut previous = tail;
     for i in 0..(OutputFields - 1) {
         // 0
@@ -748,9 +722,9 @@ pub fn slice_fields<let InputFields: u32, let OutputFields: u32>(
         // 1, 48
         let combined = previous * tail_shift + head;
         // 1, 49
-        result[i] = combined * slice_valid;
+        result[i] = combined * (slice_valid as Field);
         // 2, 51
-        previous = (tail - previous) * slice_valid + previous;
+        previous = (tail - previous) * (slice_valid as Field) + previous;
     }
 
     // 2, 130.5
@@ -787,9 +761,10 @@ pub fn slice_fields<let InputFields: u32, let OutputFields: u32>(
     std::as_witness(last_limb);
 
     let mut path: [Field; OutputFields] = [0; OutputFields];
-    path[0] = (1 - path_valid_output[0]);
+    path[0] = (1 - path_valid_output[0] as Field);
     for i in 1..OutputFields {
-        path[i] = path_valid_output[i] * -path_valid_output[i - 1] + path_valid_output[i - 1];
+        path[i] = path_valid_output[i - 1] as Field
+            - path_valid_output[i] as Field * path_valid_output[i - 1] as Field;
     }
 
     for i in 0..OutputFields {