restructured conditional prints in diff, added parabolic focus solution to quad_reg output

1 files changed, 17 insertions, 0 deletions

diff --git a/sterling_approx.awk b/sterling_approx.awk
new file mode 100644
index 0000000..5abe41d
--- /dev/null
+++ b/sterling_approx.awk
@@ -0,0 +1,17 @@
+#!/usr/bin/awk -f
+
+### sterling_approx.awk
+# https://en.wikipedia.org/wiki/Stirling%27s_approximation
+
+BEGIN {
+    ARGV[1] ? n = ARGV[1] : n = 0
+    pi = 4*atan2(1,1)
+    p = 0
+    if (n > 0) {
+        p = 1
+        for (m=n; m>0; m--)
+            p *= n*exp(-1)
+        p = sqrt(2*pi*n)*p*(1 + 1/(12*n) + 1/(288*n*n) - 139/(51840*n*n*n) - 571/(2488320*n*n*n*n))
+    }
+    printf(OFMT ORS, p)
+}