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;; Copyright (C) 2026 Thomas Guillermo Albers Raviola
;;
;; This program is free software: you can redistribute it and/or modify
;; it under the terms of the GNU General Public License as published by
;; the Free Software Foundation, either version 3 of the License, or
;; (at your option) any later version.
;;
;; This program is distributed in the hope that it will be useful,
;; but WITHOUT ANY WARRANTY; without even the implied warranty of
;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
;; GNU General Public License for more details.
;;
;; You should have received a copy of the GNU General Public License
;; along with this program. If not, see <https://www.gnu.org/licenses/>.
(import (rnrs)
(srfi srfi-1)
(srfi srfi-43))
(define (digits-of-pi n)
;; k=0 -> 3.2222222222 ...
;; k=1 -> 0.0212212212 ...
;; start vector with 3.243443443 ...
(define digits (let ((v (make-vector n 4)))
(vector-set! v 0 2)
(do ((i 2 (+ i 3)))
((>= i (vector-length v)) v)
(vector-set! v i 3))))
(define (partial-term k)
(let ([8k (* 8 k)])
(- (/ 4 (+ 8k 1)) (/ 2 (+ 8k 4)) (/ 1 (+ 8k 5)) (/ 1 (+ 8k 6)))))
(define (do-carry! v)
(do ([i (- (vector-length v) 1) (- i 1)])
((= i 0))
(when (>= (vector-ref v i) 16)
(vector-set! v (- i 1) (+ (vector-ref v (- i 1))
(fxdiv (vector-ref v i) 16)))
(vector-set! v i (fxmod (vector-ref v i) 16)))))
;; k=2 -> 0.000acef6dc ...
;; k=3 -> 0.000055038c ...
;; k=4 -> 0.00000326fe ...
(do ([k 2 (+ k 1)])
((= k n))
(let* ([a (partial-term k)]
[den (denominator a)])
(do ([i (+ k 1) (+ i 1)]
[num (fx* 16 (numerator a)) (fxmod (fx* 16 num) den)])
((>= i n))
(let ([v (vector-ref digits i)])
(vector-set! digits i (+ v (fxdiv (fx* 16 num) den)))))))
(do-carry! digits)
digits)
(define (display-digits-of-pi n)
(let ([digits (digits-of-pi (+ n 4))])
(display "3.")
(do ([i 0 (+ i 1)])
((= i n))
(display (vector-ref digits i)))
(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)))))
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