A logarithmically recursive sine

ex1.15.scm

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+(define (cube x) (* x x x))
+
+(define (p x) (- (* 3 x) (* 4 (cube x))))
+
+(define (sine angle)
+  (define (sine-with-count angle count)
+    (cond ((not (> (abs angle) 0.1))
+           (display count)
+           angle)
+          (else
+           (p (sine-with-count (/ angle 3.0) (+ 1 count))))))
+  (sine-with-count angle 0))
+
+
+;; Check that (sine pi) is approximately 0 and (sine (/ pi 2)) is approximately
+;; 1.
+
+(define pi 3.14159)
+
+1 ]=> (sine pi)
+4
+;Value: -7.85519012433511e-4
+
+1 ]=> (sine (/ pi 2))
+3
+;Value: .9999996073961978
+
+
+;; The procedure p is evaluated 5 times when (sine 12.15) is evaluated
+
+1 ]=> (sine 12.15)
+5
+;Value: -.39980345741334
+
+
+;; The process is logarithmically recursive in space and time. Because each
+;; recursive step reduces the angle by a factor of three, and because there is
+;; only one recursive call -- no tree, a tripling of the problem size (the angle
+;; argument) increases the number of steps by one and the amount of (unitless)
+;; space needed by one. Thus, growth in resource requirements is logarithmic.
+
+1 ]=> (sine 1)
+3
+;Value: .8415945650055845
+
+1 ]=> (sine 3)
+4
+;Value: .14044054819729057
+
+1 ]=> (sine 9)
+5
+;Value: .41024170125489806
+
+1 ]=> (sine 27)
+6
+;Value: .9545532565129102
+
+1 ]=> (sine 81)
+7
+;Value: -.6153887225427268
+