Here's my solution so SICP 1.19 (computing fibonacci numbers with a
doubling transform)
;; 1.19
;; T:
;; a = a + b
;; b = a
;;
;; T_pq:
;; a' = ap + (b+a)q
;; b' = bp + aq
;;
;; T_pq^2:
;; a'' = b'q + a'q + a'p
;; = (bp + aq)q + (bq + aq + ap)(p + q)
;; = bpq + aqq + bpq + apq + app + bqq + aqq + apq
;; = (a+b)2pq + (a+b)qq + a(pp + qq)
;; = a(pp+qq) + (b+a)(2pq+qq)
;;
;; b'' = b'p + a'q
;; = (bp + aq)p + (bq + aq + ap)q
;; = bpp + apq + bqq + aqq + apq
;; = b(pp+qq) + a(2pq+qq)
;;
;; Therefore, T_pq^2 = T_(pp+qq)(2pq+qq)
define fib2(n)
fib-iter(1 0 0 1 n)
define fib-iter(a b p q n)
cond
{ n = 0 } b
even?(n) fib-iter(a
b
{square(p) + square(q)}
{{ 2 * p * q } + square(q)}
{ n / 2 })
else fib-iter({{ b * q } + {a * q } + {a * p }}
{{ b * p } + {a * q }}
p
q
{ n - 1 })
I wasn't too happy with how it turned out. For comparison, here's
fib-iter in wart:
def fib-iter(a b p q n)
(if
(iso n 0)
b
even?.n
(fib-iter a
b
(+ square.p square.q)
(+ square.q (* 2 p q))
(/ n 2))
:else
(fib-iter (+ (* b q) (* a q) (* a p))
(+ (* b p) (* a q))
p
q
(- n 1)))
To me this seems more readable. The benefits of curly infix seem
entirely offset by requiring spaces around the operators. I wish it
was closer to C, like:
{b*q + a*q + a*p}
Can y'all think of a nicer way to lay out fib-iter?
Kartik
http://github.com/akkartik/wart#readme
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