Yuvaraj Athur Raghuvir wrote:
> find the nearest prime or prime power to a number.
...
> Can fpp be tacitly defined?
Personally, I do not understand what fpp is doing, so I
am not prepared to discuss how it might be implemented
tacitly, other than to mention that f^:t^:_ is somewhat
analogous to a while loop, where t is the "while test" and
f is a side-effect free function which represents the
while body. (The argument should be a complete
representation of the state manipulated by the while
loop.)
That said, here's how I might implement "find the nearest
prime or prime power to a number", tacitly:
npp=:(((i. <./)@:|@:- { ]) ,@(i.@>:&.(p:^:_1 <mailto:i.@>:&.(p:^:_1> ) ^/
[EMAIL PROTECTED]@#:))"0 <mailto:[EMAIL PROTECTED]@#:))"0>
npp i. 5 20
1 1 2 3 4 5 5 7 8 9 9 11 11 13 13 13 16 17 17 19
19 19 23 23 25 25 27 27 27 29 29 31 32 32 32 37 37 37 37 37
41 41 41 43 43 43 47 47 49 49 49 49 53 53 53 53 53 59 59 59
59 61 61 61 64 64 67 67 67 67 71 71 71 73 73 73 73 79 79 79
81 81 81 83 83 83 83 89 89 89 89 89 89 89 97 97 97 97 97 97
Since that's a bit long, here's a breakout of some phrases:
(i.@>:&.(p:^:_1 <mailto:i.@>:&.(p:^:_1> ) generates a list of relevant primes
[EMAIL PROTECTED]@#: generates a list of relevant powers
,@(x ^/ y) generates a list from the power table
(f g)y is y f (g y) [see documentation on hook]
x(i.<./)@:|@:- y finds the index of the y closest to x
x(f{])y expects x f y to be an index into y
Note, however, that for large numbers I might gain some
efficiencies by trimming the size of my intermediate
results.
Also note that I'm not doing stuff here that you are
doing in fpp. There's a good chance that you are going
somewhere that my above example is not a good illustration
for.
--
Raul
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