Add simpler method to calculate bbp formula

1 files changed, 15 insertions, 0 deletions

diff --git a/bbp.scm b/bbp.scm
index b391bd5..9865a35 100644
--- a/bbp.scm
+++ b/bbp.scm
@@ -60,3 +60,18 @@
     (newline)))
 
 (display-digits-of-pi 100)
+
+(define (digits-of-pi* n)
+  (define digits (make-vector n 0))
+  (define (term k)
+    (let ([8k (* 8 k)])
+      (/ (- (/ 4 (+ 8k 1)) (/ 2 (+ 8k 4)) (/ 1 (+ 8k 5)) (/ 1 (+ 8k 6)))
+	 (expt 16 k))))
+  ;; sum n+1 terms
+  (define sum (let loop ([k 0] [s 0])
+		(if (> k n) s (loop (+ k 1) (+ s (term k))))))
+  (let ([den (denominator sum)])
+    (do ([i 0 (+ i 1)]
+	 [num (numerator sum) (* 16 (mod num den))])
+	((>= i n) digits)
+      (vector-set! digits i (div num den)))))