diff options
Diffstat (limited to 'bbp.scm')
| -rw-r--r-- | bbp.scm | 62 |
1 files changed, 62 insertions, 0 deletions
@@ -0,0 +1,62 @@ +;; 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) |