sicp/zapiski/sqrt-newton.scm

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2024-04-30 19:18:58 +02:00
(define (sqrt-iter guess x)
(if (good-enough? guess x)
guess
(sqrt-iter (improve guess x)
x
)
)
)
(define (improve guess x)
(average guess (/ x guess))
)
(define (average x y)
(/ (+ x y) 2)
)
(define (square x) (* x x))
(define (good-enough? guess x)
(< (abs (- (square guess) x)) 0.001)
)
(define (sqrt x)
(sqrt-iter 1.0 x)
)
(define (new-if predicate then-clause else-clause)
(cond (predicate then-clause)
(else else-clause)
)
)
(define (new-sqrt-iter guess x)
"gre v neskoncni loop"
(new-if (good-enough? guess x)
guess
(new-sqrt-iter (improve guess x)
x
)
)
)
(define (abs x)
(if (> 0 x) (- x) x)
)
(define (better-enough? g1 g2)
"Sledimo spremembam priblizkov. Ustavimo, ko je sprememba majhen delez priblizka."
(< (/ (- g1 g2) g1) 0.0001)
)
(define (better-sqrt-iter guess x)
"Better sqrt. Naloga 1.8."
(let ((g2 (improve guess x)))
(if (better-enough? g2 guess)
g2
(better-sqrt-iter g2 x)
)
)
)
(define (improve-cube-root guess x)
(/ (+ (* 2 guess) (/ x (* guess guess))) 3)
)
(define (cube-root-iter guess x)
"Tretji koren"
(if (good-enough? guess x)
guess
(cube-root-iter (improve-cube-root guess x) x)
)
)