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| -rw-r--r-- | net/ricketyspace/sicp/two/thirteen.scm | 48 |
1 files changed, 48 insertions, 0 deletions
diff --git a/net/ricketyspace/sicp/two/thirteen.scm b/net/ricketyspace/sicp/two/thirteen.scm new file mode 100644 index 0000000..8744901 --- /dev/null +++ b/net/ricketyspace/sicp/two/thirteen.scm @@ -0,0 +1,48 @@ +;;;; 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 |