Add (net ricketyspace sicp two thirteen).

* net/ricketyspace/sicp/two/thirteen.scm: New file.

1 files changed, 48 insertions, 0 deletions

diff --git a/net/ricketyspace/sicp/two/thirteen.scm b/net/ricketyspace/sicp/two/thirteen.scm
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+;;;; Under Creative Commons Attribution-ShareAlike 4.0
+;;;; International. See
+;;;; <https://creativecommons.org/licenses/by-sa/4.0/>.
+
+(define-module (net ricketyspace sicp two thirteen)
+  #:use-module (net ricketyspace sicp two twelve)
+  #:export (mul-tol-percent))
+
+(define (mul-tol-percent intv-a intv-b)
+  "Returns approx. percentage tolerance of INT-A * INTV-B.
+
+Assumes all numbers in INTV-A and INTV-B are positive.
+
+Say 2⨦.10 and 7⨦.20 are the two intervals.
+
+  The lower and upper bounds of the product of these interavals:
+
+     (2 - 0.10) * (7 - 0.20) ; Lower bound
+     (2 - 0.10) * (7 - 0.20) ; Upper bound
+
+      Lower bound -> (2 - 0.10) * (7 - 0.20)
+                  -> (2 * 7) - (2 * 0.20) - (7 * 0.10) + (0.10 * 0.20)
+                                   X            Y            Z
+                  -> (2 * 7) - (X + Y - Z)
+                  -> (2 * 7) - (X + Y) ; ignore Z as it is small.
+
+      Upper bound -> (2 + 0.10) * (7 + 0.20)
+                  -> (2 * 7) + (2 * 0.20) + (7 * 0.10) + (0.10 * 0.20)
+                                   X            Y            Z
+                  -> (2 * 7) - (X + Y + Z)
+                  -> (2 * 7) - (X + Y)  ; ignore Z as it is small.
+
+      => Percentage tolerance is ⨦ (X + Y)"
+  (let* ((ca (center intv-a))
+         (pa (percent intv-a))
+         (cb (center intv-b))
+         (pb (percent intv-b))
+         (x (* ca pb))
+         (y (* cb pa)))
+      (/ (+ x y) 100.0)))
+
+
+;;; Guile REPL
+;;; scheme@(guile-user)> ,re  (net ricketyspace sicp two thirteen)
+;;; scheme@(guile-user)> (mul-tol-percent (make-center-percent 2 10) (make-center-percent 7 20))
+;;; $20 = 1.1000000000000003
+;;; scheme@(guile-user)> (+ (* 2 .20) (* 0.10 7))
+;;; $21 = 1.1