# nie-ii-year

lab stuff from undergrad second year.
git clone http://git.hanabi.in/repos/nie-ii-year.git
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commit f99c8574a3a063f67f6d47536d60ed85b871c807
parent 32c9a8575315fa4643efa594e8d6cc5c7546f484
Author: Agastya Chandrakant <acagastya@outlook.com>
Date:   Mon, 16 Apr 2018 20:18:45 +0530

Diffstat:
Ms4/fafl/report.md | 25++++++++++++++++++++++++-

1 file changed, 24 insertions(+), 1 deletion(-)
diff --git a/s4/fafl/report.md b/s4/fafl/report.md
@@ -4,9 +4,32 @@
## Standard TM to compute modulo and division of two natural numbers as well as to check if a given natural number is prime
### STM as a transducer to compute modulo and division

-Consider two numbers u and v. u % v = (u - v) % v, if u > v else u. Using this, a recursive relation can be established, which is:
+Consider two numbers u and v. u % v = (u - v) % v, if u is greater than or equal to v else u. Using this, a recursive relation can be established, which is:
$\mod(u, v) = \begin{cases} u: u < v\\mod (u - v, v): otherwise\end{cases}$

+Its iteratie code in JavaScript is:
+
+
+function modulo(u, v) {
+  while(u >= v)
+    u = u - v;
+  return u;
+}
+
+Repeatedly subtracting yields remainder. However, if we count the number of times subtraction was performed, we get the quotient. Hence, modifying the above code slightly, quotient can be calculated:
+
+
+function newModulo(u, v) {
+  var quo = 0;
+  while(u >= v) {
+    u = u - v;
+    quo++;
+  }
+  return u;
+}
+
+In the above code, quo variable gives the
+
### 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 $\frac{num}{2}$