From c13f497cdf68d53ce087cc1e57db6b3047d46616 Mon Sep 17 00:00:00 2001
From: rsiddharth <s@ricketyspace.net>
Date: Sat, 14 Oct 2017 03:10:24 +0000
Subject: (net ricketyspace sicp one thirtyone): Add iterative version.

* net/ricketyspace/sicp/one/thirtyone.scm
(product-iter, factorial-iter, pi-iter): New functions.
---
 net/ricketyspace/sicp/one/thirtyone.scm | 52 ++++++++++++++++++++++++++-------
 1 file changed, 42 insertions(+), 10 deletions(-)

diff --git a/net/ricketyspace/sicp/one/thirtyone.scm b/net/ricketyspace/sicp/one/thirtyone.scm
index a88dc1d..f84f637 100644
--- a/net/ricketyspace/sicp/one/thirtyone.scm
+++ b/net/ricketyspace/sicp/one/thirtyone.scm
@@ -3,7 +3,7 @@
 ;;;; <https://creativecommons.org/licenses/by-sa/4.0/>.
 
 (define-module (net ricketyspace sicp one thirtyone)
-  #:export (product factorial pi))
+  #:export (product product-iter factorial factorial-iter pi pi-iter))
 
 (define (product term a next b)
   (if (> a b)
@@ -11,11 +11,23 @@
       (* (term a)
          (product term (next a) next b))))
 
+(define (product-iter term a next b)
+  (define (iter a result)
+    (if (> a b)
+        result
+        (iter (next a) (* (term a) result))))
+  (iter a 1))
+
 (define (factorial n)
   (let ((term (lambda (x) x))
         (next (lambda (x) (1+ x))))
     (product term 1 next n)))
 
+(define (factorial-iter n)
+  (let ((term (lambda (x) x))
+        (next (lambda (x) (1+ x))))
+    (product-iter term 1 next n)))
+
 (define (pi precision)
   (let* ((n (lambda (x) (* (+ (quotient x 2) 1) 2))) ; numerator of term.
          (d (lambda (x) (+ (* (quotient (1+ x) 2) 2) 1))) ; denominator of term.
@@ -23,21 +35,41 @@
          (next (lambda (x) (1+ x))))
     (* (product term 1 next precision) 4)))
 
+(define (pi-iter precision)
+  (let* ((n (lambda (x) (* (+ (quotient x 2) 1) 2))) ; numerator of term.
+         (d (lambda (x) (+ (* (quotient (1+ x) 2) 2) 1))) ; denominator of term.
+         (term (lambda (x) (/ (* (n x) 1.0) (* (d x) 1.0))))
+         (next (lambda (x) (1+ x))))
+    (* (product-iter term 1 next precision) 4)))
+
+
 ;;; Guile REPL
 ;;; scheme@(guile-user)> ,use (net ricketyspace sicp one thirtyone)
 ;;; scheme@(guile-user)> (factorial 5)
-;;; $9 = 120
+;;; $19 = 120
+;;; scheme@(guile-user)> (factorial-iter 5)
+;;; $20 = 120
 ;;; scheme@(guile-user)> (factorial 10)
-;;; $7 = 3628800
+;;; $21 = 3628800
+;;; scheme@(guile-user)> (factorial-iter 10)
+;;; $22 = 3628800
 ;;; scheme@(guile-user)> (factorial 20)
-;;; $8 = 2432902008176640000
+;;; $23 = 2432902008176640000
+;;; scheme@(guile-user)> (factorial-iter 20)
+;;; $24 = 2432902008176640000
 ;;; scheme@(guile-user)> (pi 1000)
-;;; $10 = 3.143160705532257
+;;; $25 = 3.143160705532257
+;;; scheme@(guile-user)> (pi-iter 1000)
+;;; $26 = 3.1431607055322552
 ;;; scheme@(guile-user)> (pi 10000)
-;;; $11 = 3.1417497057379635
+;;; $27 = 3.1417497057379635
+;;; scheme@(guile-user)> (pi-iter 10000)
+;;; $28 = 3.1417497057380084
 ;;; scheme@(guile-user)> (pi 100000)
-;;; $12 = 3.1416083612780903
+;;; $29 = 3.1416083612780903
+;;; scheme@(guile-user)> (pi-iter 100000)
+;;; $30 = 3.141608361277941
 ;;; scheme@(guile-user)> (pi 1000000)
-;;; $13 = 3.1415942243828017
-
-
+;;; $31 = 3.1415942243828017
+;;; scheme@(guile-user)> (pi-iter 1000000)
+;;; $32 = 3.141594224382854
-- 
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