nie-ii-year

commit 01e9a16dbd662d0bb5ff777601297452eae8a393
parent a573111c587fa6e98050a005b3cdf663feff4bef
Author: Agastya Chandrakant <acagastya@outlook.com>
Date:   Mon, 16 Apr 2018 22:04:39 +0530

add
Diffstat:
M
s4/fafl/report.md
 | 
11
+++++++++--

1 file changed, 9 insertions(+), 2 deletions(-)
diff --git a/s4/fafl/report.md b/s4/fafl/report.md
@@ -34,7 +34,7 @@ __Refer figure 1 for TM1 which acts as a transducer to find remainder and quotie
 
 ### STM to check if entered natural number is prime or not
 
-Consider a natural number `num`. If it is a composite number, it has atleast one factor between two and $\frac{num}{2}$, boh inclusive.
+Consider a natural number `num`. If it is a composite number, it has atleast one factor between two and $\frac{num}{2}$, both inclusive.
 
 __Refer figure 2 for TM1 which acts as a transducer to find remainder and quotient of two natural numbers__
 
@@ -50,7 +50,7 @@ __Refer figure 2 for TM1 which acts as a transducer to find remainder and quotie
 Since calculation of modulo is subtracion of `v` from `u` until `u` is strictly smaller than `v`, procedure to follow `u - v` is as follows: (__Assumption: Instruction pointer points to index 1__)
 
 1. While current cell value is not `0`, move right.
-2. If current cell value is `0`, go left. If it is `1`: Go right. Go right.
+2. If current cell value is `0`, go left. If it is `1`: Go right. Go right. Else, goto step #3
     - If it is `1`:
         - Go right until current cell is `B`.
         - Move left until current cell is `1`.
@@ -60,6 +60,13 @@ Since calculation of modulo is subtracion of `v` from `u` until `u` is strictly 
     - If it is `X`, one subtraction is finished. (It's progress can be tracked, which will be mentioned later while dealing with quotient)
         - Go right making all `X` as `1` until current cell is `B`.
         - if current cell is `B` go left until current cell is `0`. Goto step #2.
+3. If the current cell is `B`, go right, go right. If current cell is `X`, modulo is `0`. Stop. Else, goto step #4.
+4. Having travelled two right from reading `B`, if the current cell is `1`, it simply means LHS number was smaller than RHS. In that case:
+    - Move right until current cell is `X`.
+    - Make current cell as `1`.
+    - Goto right until current cell is `B`.
+    - Make `B` as `1`. Repeat these four sub-steps until instruction pointer reaches `B` on the right hand side.
+        
 #### To find if the number is prime
 
 For an input `num`, the first step is to make a copy of $\lfloor\dfrac{num}{2}\rfloor$ start reading the tape from the beginning. (__Assumption: Instruction pointer points to index 0__)