Add guile/taocp/one/two/eight/fib.scm

1 files changed, 361 insertions, 0 deletions

diff --git a/guile/taocp/one/two/eight/fib.scm b/guile/taocp/one/two/eight/fib.scm
new file mode 100644
index 0000000..b26d392
--- /dev/null
+++ b/guile/taocp/one/two/eight/fib.scm
@@ -0,0 +1,361 @@
+;;;; copyright 2016 rsiddharth <s@ricketyspace.net>
+;;;; under gnu general public license version 3 or higher.
+
+(define-module (taocp one two eight fib)
+  #:use-module (srfi srfi-1)
+  #:export (fib-fast
+            fib-1-1000))
+
+(define phi
+  (/ (+ 1 (sqrt 5.0)) 2.0))
+
+(define phi-dash
+  (/ (- 1 (sqrt 5.0)) 2.0))
+
+(define (fib-fast n)
+  "compute fibonacci of `n`."
+  (/ (-  (expt phi n) (expt phi-dash n))
+     (sqrt 5.0)))
+
+(define (fib-1-1000)
+  "return fibonacci numbers between 1 and 1000."
+  (reverse (fold (lambda (n prev)
+                   (cons (fib-fast n) prev))
+                 '()
+                 (iota 1000 0))))
+
+
+;; scheme@(taocp one two eight fib)> (fib-1-1000)
+;; $39 = (0.0 1.0 1.0 2.0 3.0 5.0 8.0 13.0 21.0 34.0 54.99999999999999
+;; 89.0 143.99999999999997 232.99999999999994 377.00000000000006 610.0
+;; 986.9999999999998 1596.9999999999998 2584.0 4181.0
+;; 6764.999999999999 10945.999999999998 17710.999999999996
+;; 28656.999999999996 46367.99999999999 75025.0 121392.99999999999
+;; 196418.0 317811.0 514228.99999999994 832039.9999999999
+;; 1346268.9999999998 2178309.0 3524577.9999999995 5702886.999999999
+;; 9227465.0 14930351.999999998 24157816.999999996 39088168.99999999
+;; 63245985.99999999 102334154.99999999 165580140.99999997
+;; 267914295.99999994 433494437.0 701408732.9999999 1134903169.9999998
+;; 1836311903.0 2971215072.9999995 4807526975.999999 7778742048.999998
+;; 12586269024.999998 20365011074.0 32951280098.999992
+;; 53316291172.999985 86267571271.99998 139583862444.99997
+;; 225851433716.99997 365435296161.99994 591286729878.9999
+;; 956722026040.9999 1548008755919.9998 2504730781960.9995
+;; 4052739537880.999 6557470319841.999 10610209857722.998
+;; 17167680177564.996 27777890035287.996 44945570212852.99
+;; 72723460248140.98 117669030460993.98 190392490709134.97
+;; 308061521170129.0 498454011879263.9 806515533049392.9
+;; 1304969544928656.8 2111485077978049.5 3416454622906706.0
+;; 5527939700884755.0 8944394323791463.0 14472334024676218.0
+;; 23416728348467676.0 37889062373143896.0 61305790721611580.0
+;; 99194853094755490.0 160500643816367040.0 259695496911122530.0
+;; 420196140727489600.0 679891637638612100.0 1100087778366101600.0
+;; 1779979416004713700.0 2880067194370815500.0 4660046610375529000.0
+;; 7540113804746344000.0 12200160415121873000.0 19740274219868217000.0
+;; 3.194043463499009e19 5.16807088548583e19 8.362114348984841e19
+;; 1.353018523447067e20 2.1892299583455514e20 3.542248481792618e20
+;; 5.731478440138169e20 9.273726921930788e20 1.5005205362068957e21
+;; 2.4278932283999744e21 3.9284137646068696e21 6.356306993006844e21
+;; 1.0284720757613714e22 1.664102775062056e22 2.692574850823427e22
+;; 4.356677625885483e22 7.04925247670891e22 1.1405930102594392e23
+;; 1.84551825793033e23 2.9861112681897695e23 4.831629526120101e23
+;; 7.81774079430987e23 1.2649370320429967e24 2.0467111114739838e24
+;; 3.3116481435169805e24 5.358359254990965e24 8.670007398507945e24
+;; 1.402836665349891e25 2.2698374052006855e25 3.6726740705505764e25
+;; 5.942511475751263e25 9.615185546301839e25 1.55576970220531e26
+;; 2.517288256835494e26 4.0730579590408044e26 6.590346215876297e26
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