So I want to find the sum of applying function f to the first n integers, when the sum of applying f to the first n integers is f applied to n plus the sum of applying f to the first n-1 integers, as in:
- fun inc x = x+1;
> val inc = fn : inet -> int
- sumF inc 3;
> 9 : int i.e. inc 3+inc 2+ inc 1+ 0
and my sumF looks like this now:
- fun sumF 0 = 0 | sumF n = sumF(n) + sumF(n-1);
val sumF = fn : int -> int
- sumF inc 3;
stdIn:15.1-15.11 Error: operator and operand don't agree [tycon mismatch]
operator domain: int
operand: int -> int
in expression:
sumF inc
As you can see I get an error, so maybe anyone knows how to fix it? Because later on, I want to write sumSq (sumSq n = (nn) + sumSq(n-1)) and sumHalf (sumSq n = (nn) + sumSq(n-1)), using sumF.
Thanks!
Here is a possible solution:
fun sumF f 0 = 0
| sumF f n = f n + sumF f (n - 1)
Your problem is, that you don't actually use the inc function in the definition of sumF function. You define the sumF function with only one argument of type int, but then you call this function with "two arguments". Your function call sumF inc 3 is interpreted as ((sumF inc) 3), and since the type of inc is int -> int, but the function expects the argument of type int, you get the error. And, besides this, your function has an additional problem - it creates infinite loop, since you call sumF n in the definition of sumF n.
You can call the function above as
- fun inc x = x + 1;
val inc = fn : int -> int
- sumF inc 3;
val it = 9 : int
or a bit shorter with anonymous function:
- sumF (fn x => x + 1) 3;
val it = 9 : int
Regards, Špela
Related
I need to create a function that takes a number, such as for a given number x, it computes the number y, by adding all digits of number x to itself.
An example :
Given x = 123:
It return 129 = 1 + 2 + 3 + 123
Given x = 35:
It return y = 43 = 3 + 5 + 35
I have this function that works but I need another way:
computeNextValue : Int -> Int
computeNextValue input =
String.fromInt input
|> String.split ""
|> List.filterMap String.toInt
|> List.sum
|> (+) input
First, let's make a recursive function that gives you all the digits of a number. The main idea is that you can get the rightmost digit of an integer by modBy 10, and you can remove it from the number by // 10:
getDigits : Int -> List Int
getDigits num =
if num == 0 then
[] -- base case
else
modBy 10 num :: getDigits (num // 10) -- recursive case
Note that this function returns the [] for 0, but that's OK for this usecase.
computeNextValue : Int -> Int
computeNextValue input =
input + List.sum (getDigits inputs)
I am currently trying to refresh my Haskell knowledge by solving some Hackerrank problems.
For example:
https://www.hackerrank.com/challenges/maximum-palindromes/problem
I've already implemented an imperative solution in C++ which got accepted for all test cases. Now I am trying to come up with a pure functional solution in (reasonably idiomatic) Haskell.
My current code is
module Main where
import Control.Monad
import qualified Data.ByteString.Char8 as C
import Data.Bits
import Data.List
import qualified Data.Map.Strict as Map
import qualified Data.IntMap.Strict as IntMap
import Debug.Trace
-- precompute factorials
compFactorials :: Int -> Int -> IntMap.IntMap Int
compFactorials n m = go 0 1 IntMap.empty
where
go a acc map
| a < 0 = map
| a < n = go a' acc' map'
| otherwise = map'
where
map' = IntMap.insert a acc map
a' = a + 1
acc' = (acc * a') `mod` m
-- precompute invs
compInvs :: Int -> Int -> IntMap.IntMap Int -> IntMap.IntMap Int
compInvs n m facts = go 0 IntMap.empty
where
go a map
| a < 0 = map
| a < n = go a' map'
| otherwise = map'
where
map' = IntMap.insert a v map
a' = a + 1
v = (modExp b (m-2) m) `mod` m
b = (IntMap.!) facts a
modExp :: Int -> Int -> Int -> Int
modExp b e m = go b e 1
where
go b e r
| (.&.) e 1 == 1 = go b' e' r'
| e > 0 = go b' e' r
| otherwise = r
where
r' = (r * b) `mod` m
b' = (b * b) `mod` m
e' = shift e (-1)
-- precompute frequency table
initFreqMap :: C.ByteString -> Map.Map Char (IntMap.IntMap Int)
initFreqMap inp = go 1 map1 map2 inp
where
map1 = Map.fromList $ zip ['a'..'z'] $ repeat 0
map2 = Map.fromList $ zip ['a'..'z'] $ repeat IntMap.empty
go idx m1 m2 inp
| C.null inp = m2
| otherwise = go (idx+1) m1' m2' $ C.tail inp
where
m1' = Map.update (\v -> Just $ v+1) (C.head inp) m1
m2' = foldl' (\m w -> Map.update (\v -> liftM (\c -> IntMap.insert idx c v) $ Map.lookup w m1') w m)
m2 ['a'..'z']
query :: Int -> Int -> Int -> Map.Map Char (IntMap.IntMap Int)
-> IntMap.IntMap Int -> IntMap.IntMap Int -> Int
query l r m freqMap facts invs
| x > 1 = (x * y) `mod` m
| otherwise = y
where
calcCnt cs = cr - cl
where
cl = IntMap.findWithDefault 0 (l-1) cs
cr = IntMap.findWithDefault 0 r cs
f1 acc cs
| even cnt = acc
| otherwise = acc + 1
where
cnt = calcCnt cs
f2 (acc1,acc2) cs
| cnt < 2 = (acc1 ,acc2)
| otherwise = (acc1',acc2')
where
cnt = calcCnt cs
n = cnt `div` 2
acc1' = acc1 + n
r = choose acc1' n
acc2' = (acc2 * r) `mod` m
-- calc binomial coefficient using Fermat's little theorem
choose n k
| n < k = 0
| otherwise = (f1 * t) `mod` m
where
f1 = (IntMap.!) facts n
i1 = (IntMap.!) invs k
i2 = (IntMap.!) invs (n-k)
t = (i1 * i2) `mod` m
x = Map.foldl' f1 0 freqMap
y = snd $ Map.foldl' f2 (0,1) freqMap
main :: IO()
main = do
inp <- C.getLine
q <- readLn :: IO Int
let modulo = 1000000007
let facts = compFactorials (C.length inp) modulo
let invs = compInvs (C.length inp) modulo facts
let freqMap = initFreqMap inp
forM_ [1..q] $ \_ -> do
line <- getLine
let [s1, s2] = words line
let l = (read s1) :: Int
let r = (read s2) :: Int
let result = query l r modulo freqMap facts invs
putStrLn $ show result
It passes all small and medium test cases but I am getting timeout with large test cases.
The key to solve this problem is to precompute some stuff once at the beginning and use them to answer the individual queries efficiently.
Now, my main problem where I need help is:
The initital profiling shows that the lookup operation of the IntMap seems to be the main bottleneck. Is there better alternative to IntMap for memoization? Or should I look at Vector or Array, which I believe will lead to more "ugly" code.
Even in current state, the code doesn't look nice (by functional standards) and as verbose as my C++ solution. Any tips to make it more idiomatic? Other than IntMap usage for memoization, do you spot any other obvious problems which can lead to performance problems?
And is there any good sources, where I can learn how to use Haskell more effectively for competitive programming?
A sample large testcase, where the current code gets timeout:
input.txt
output.txt
For comparison my C++ solution:
#include <vector>
#include <iostream>
#define MOD 1000000007L
long mod_exp(long b, long e) {
long r = 1;
while (e > 0) {
if ((e & 1) == 1) {
r = (r * b) % MOD;
}
b = (b * b) % MOD;
e >>= 1;
}
return r;
}
long n_choose_k(int n, int k, const std::vector<long> &fact_map, const std::vector<long> &inv_map) {
if (n < k) {
return 0;
}
long l1 = fact_map[n];
long l2 = (inv_map[k] * inv_map[n-k]) % MOD;
return (l1 * l2) % MOD;
}
int main() {
std::string s;
int q;
std::cin >> s >> q;
std::vector<std::vector<long>> freq_map;
std::vector<long> fact_map(s.size()+1);
std::vector<long> inv_map(s.size()+1);
for (int i = 0; i < 26; i++) {
freq_map.emplace_back(std::vector<long>(s.size(), 0));
}
std::vector<long> acc_map(26, 0);
for (int i = 0; i < s.size(); i++) {
acc_map[s[i]-'a']++;
for (int j = 0; j < 26; j++) {
freq_map[j][i] = acc_map[j];
}
}
fact_map[0] = 1;
inv_map[0] = 1;
for (int i = 1; i <= s.size(); i++) {
fact_map[i] = (i * fact_map[i-1]) % MOD;
inv_map[i] = mod_exp(fact_map[i], MOD-2) % MOD;
}
while (q--) {
int l, r;
std::cin >> l >> r;
std::vector<long> x(26, 0);
long t = 0;
long acc = 0;
long result = 1;
for (int i = 0; i < 26; i++) {
auto cnt = freq_map[i][r-1] - (l > 1 ? freq_map[i][l-2] : 0);
if (cnt % 2 != 0) {
t++;
}
long n = cnt / 2;
if (n > 0) {
acc += n;
result *= n_choose_k(acc, n, fact_map, inv_map);
result = result % MOD;
}
}
if (t > 0) {
result *= t;
result = result % MOD;
}
std::cout << result << std::endl;
}
}
UPDATE:
DanielWagner's answer has confirmed my suspicion that the main problem in my code was the usage of IntMap for memoization. Replacing IntMap with Array made my code perform similar to DanielWagner's solution.
module Main where
import Control.Monad
import Data.Array (Array)
import qualified Data.Array as A
import qualified Data.ByteString.Char8 as C
import Data.Bits
import Data.List
import Debug.Trace
-- precompute factorials
compFactorials :: Int -> Int -> Array Int Int
compFactorials n m = A.listArray (0,n) $ scanl' f 1 [1..n]
where
f acc a = (acc * a) `mod` m
-- precompute invs
compInvs :: Int -> Int -> Array Int Int -> Array Int Int
compInvs n m facts = A.listArray (0,n) $ map f [0..n]
where
f a = (modExp ((A.!) facts a) (m-2) m) `mod` m
modExp :: Int -> Int -> Int -> Int
modExp b e m = go b e 1
where
go b e r
| (.&.) e 1 == 1 = go b' e' r'
| e > 0 = go b' e' r
| otherwise = r
where
r' = (r * b) `mod` m
b' = (b * b) `mod` m
e' = shift e (-1)
-- precompute frequency table
initFreqMap :: C.ByteString -> Map.Map Char (Array Int Int)
initFreqMap inp = Map.fromList $ map f ['a'..'z']
where
n = C.length inp
f c = (c, A.listArray (0,n) $ scanl' g 0 [0..n-1])
where
g x j
| C.index inp j == c = x+1
| otherwise = x
query :: Int -> Int -> Int -> Map.Map Char (Array Int Int)
-> Array Int Int -> Array Int Int -> Int
query l r m freqMap facts invs
| x > 1 = (x * y) `mod` m
| otherwise = y
where
calcCnt freqMap = cr - cl
where
cl = (A.!) freqMap (l-1)
cr = (A.!) freqMap r
f1 acc cs
| even cnt = acc
| otherwise = acc + 1
where
cnt = calcCnt cs
f2 (acc1,acc2) cs
| cnt < 2 = (acc1 ,acc2)
| otherwise = (acc1',acc2')
where
cnt = calcCnt cs
n = cnt `div` 2
acc1' = acc1 + n
r = choose acc1' n
acc2' = (acc2 * r) `mod` m
-- calc binomial coefficient using Fermat's little theorem
choose n k
| n < k = 0
| otherwise = (f1 * t) `mod` m
where
f1 = (A.!) facts n
i1 = (A.!) invs k
i2 = (A.!) invs (n-k)
t = (i1 * i2) `mod` m
x = Map.foldl' f1 0 freqMap
y = snd $ Map.foldl' f2 (0,1) freqMap
main :: IO()
main = do
inp <- C.getLine
q <- readLn :: IO Int
let modulo = 1000000007
let facts = compFactorials (C.length inp) modulo
let invs = compInvs (C.length inp) modulo facts
let freqMap = initFreqMap inp
replicateM_ q $ do
line <- getLine
let [s1, s2] = words line
let l = (read s1) :: Int
let r = (read s2) :: Int
let result = query l r modulo freqMap facts invs
putStrLn $ show result
I think you've shot yourself in the foot by trying to be too clever. Below I'll show a straightforward implementation of a slightly different algorithm that is about 5x faster than your Haskell code.
Here's the core combinatoric computation. Given a character frequency count for a substring, we can compute the number of maximum-length palindromes this way:
Divide all the frequencies by two, rounding down; call this the div2-frequencies. We'll also want the mod2-frequencies, which is the set of letters for which we had to round down.
Sum the div2-frequencies to get the total length of the palindrome prefix; its factorial gives an overcount of the number of possible prefixes for the palindrome.
Take the product of the factorials of the div2-frequencies. This tells the factor by which we overcounted above.
Take the size of the mod2-frequencies, or choose 1 if there are none. We can extend any of the palindrome prefixes by one of the values in this set, if there are any, so we have to multiply by this size.
For the overcounting step, it's not super obvious to me whether it would be faster to store precomputed inverses for factorials, and take their product, or whether it's faster to just take the product of all the factorials and do one inverse operation at the very end. I'll do the latter, because it just intuitively seems faster to do one inversion per query than one lookup per repeated letter, but what do I know? Should be easy to test if you want to try to adapt the code yourself.
There's only one other quick insight I had vs. your code, which is that we can cache the frequency counts for prefixes of the input; then computing the frequency count for a substring is just pointwise subtraction of two cached counts. Your precomputation on the input I find to be a bit excessive in comparison.
Without further ado, let's see some code. As usual there's some preamble.
module Main where
import Control.Monad
import Data.Array (Array)
import qualified Data.Array as A
import Data.Map.Strict (Map)
import qualified Data.Map.Strict as M
import Data.Monoid
Like you, I want to do all my computations on cheap Ints and bake in the modular operations where possible. I'll make a newtype to make sure this happens for me.
newtype Mod1000000007 = Mod Int deriving (Eq, Ord)
instance Num Mod1000000007 where
fromInteger = Mod . (`mod` 1000000007) . fromInteger
Mod l + Mod r = Mod ((l+r) `rem` 1000000007)
Mod l * Mod r = Mod ((l*r) `rem` 1000000007)
negate (Mod v) = Mod ((1000000007 - v) `rem` 1000000007)
abs = id
signum = id
instance Integral Mod1000000007 where
toInteger (Mod n) = toInteger n
quotRem a b = (a * b^1000000005, 0)
I baked in the base of 1000000007 in several places, but it's easy to generalize by giving Mod a phantom parameter and making a HasBase class to pick the base. Ask a fresh question if you're not sure how and are interested; I'll be happy to do a more thorough writeup. There's a few more instances for Mod that are basically uninteresting and primarily needed because of Haskell's wacko numeric class hierarchy:
instance Show Mod1000000007 where show (Mod n) = show n
instance Real Mod1000000007 where toRational (Mod n) = toRational n
instance Enum Mod1000000007 where
toEnum = Mod . (`mod` 1000000007)
fromEnum (Mod n) = n
Here's the precomputation we want to do for factorials...
type FactMap = Array Int Mod1000000007
factMap :: Int -> FactMap
factMap n = A.listArray (0,n) (scanl (*) 1 [1..])
...and for precomputing frequency maps for each prefix, plus getting a frequency map given a start and end point.
type FreqMap = Map Char Int
freqMaps :: String -> Array Int FreqMap
freqMaps s = go where
go = A.listArray (0, length s)
(M.empty : [M.insertWith (+) c 1 (go A.! i) | (i, c) <- zip [0..] s])
substringFreqMap :: Array Int FreqMap -> Int -> Int -> FreqMap
substringFreqMap maps l r = M.unionWith (-) (maps A.! r) (maps A.! (l-1))
Implementing the core computation described above is just a few lines of code, now that we have suitable Num and Integral instances for Mod1000000007:
palindromeCount :: FactMap -> FreqMap -> Mod1000000007
palindromeCount facts freqs
= toEnum (max 1 mod2Freqs)
* (facts A.! sum div2Freqs)
`div` product (map (facts A.!) div2Freqs)
where
(div2Freqs, Sum mod2Freqs) = foldMap (\n -> ([n `quot` 2], Sum (n `rem` 2))) freqs
Now we just need a short driver to read stuff and pass it around to the appropriate functions.
main :: IO ()
main = do
inp <- getLine
q <- readLn
let freqs = freqMaps inp
facts = factMap (length inp)
replicateM_ q $ do
[l,r] <- map read . words <$> getLine
print . palindromeCount facts $ substringFreqMap freqs l r
That's it. Notably I made no attempt to be fancy about bitwise operations and didn't do anything fancy with accumulators; everything is in what I would consider idiomatic purely-functional style. The final count is about half as much code that runs about 5x faster.
P.S. Just for fun, I replaced the last line with print (l+r :: Int)... and discovered that about half the time is spent in read. Ouch! Seems there's still plenty of low-hanging fruit if this isn't fast enough yet.
The specific binary search implementation is shown as below. The question I want to ask is that is it possible for the algorithm to run into infinite loop?
One possible situation I could think of is when l == r == UINT_MAX and the target x is larger than all elements in the array. Is it true that under this situation, the algorithm will stuck in infinite loop?
Are there any other situations of running into infinite loop?
Thanks for your help!!!
// A iterative binary search function. It returns location of x in
// given array arr[l..r] if present, otherwise -1.
int binarySearch(vector<double> arr, double x) {
unsigned int l = 0;
unsigned int r = arr.size() - 1;
while (l <= r) {
int m = l + (r - l) / 2;
if (arr[m] == x)
return m;
if (arr[m] < x)
l = m + 1;
else
r = m - 1;
}
return -1;
}
No it doesn't! An infinite loop only happens here if l and r could possibly stay on the same value forever. For that to happen, one of these things need to happen:
1) new value of l = old value of l:
m + 1 = l + (r - l) / 2 + 1 = l --> (r - l)/2 + 1 = 0 (which never happens since the left side is always positive knowing that r is already bigger equal than l)
2) new value of r = old value of r:
m - 1 = l + (r - l) / 2 - 1 = r --> (r - l)/2 = r - l + 1 (this also never happens because the right side is always strictly bigger)
I have been tried to do the Morris Pratt table and the code is basically this one in C:
void preMp(char *x, int m, int mpNext[]) {
int i, j;
i = 0;
j = mpNext[0] = -1;
while (i < m) {
while (j > -1 && x[i] != x[j])
j = mpNext[j];
mpNext[++i] = ++j;
}
}
and here is where i get so far in Fortran
program MP_ALGORITHM
implicit none
integer, parameter :: m=4
character(LEN=m) :: x='abac'
integer, dimension(4) :: T
integer :: i, j
i=0
T(1)=-1
j=-1
do while(i < m)
do while((j > -1) .AND. (x(i+1:i+1) /= (x(j+i+1:j+i+1))))
j=T(j)
end do
i=i+1
j=j+1
T(i)=j
end do
print *, T(1:)
end program MP_ALGORITHM
and the problem is i think i am having the wrong output.
for x=abac it should be (?):
a b a c
-1 0 1 0
and my code is returning 0 1 1 1
so, what i've done wrong?
The problem here is that C indices start from zero, but Fortran indices start from one. You can try to adjust the index for every array acces by one, but this will get unwieldy.
The Morris-Pratt table itself is an array of indices, so it should look different in C and Fortran: The Fortran array should have one-based indices and it should use zero as invalid index.
Together with the error that chw21 pointed out, your function might look like this:
subroutine kmp_table(x, t)
implicit none
character(*), intent(in) :: x
integer, dimension(:), intent(out) :: t
integer m
integer :: i, j
m = len(x)
i = 1
t(1) = 0
j = 0
do while (i < m)
do while(j > 0 .and. x(i:i) /= x(j:j))
j = t(j)
end do
i = i + 1
j = j + 1
t(i) = j
end do
end subroutine
You can then use it in the Morris-Pratt algorithm as taken straight from the Wikipedia page with adjustment for Fortran indices:
function kmp_index(S, W) result(res)
implicit none
integer :: res
character(*), intent(in) :: S ! text to search
character(*), intent(in) :: W ! word to find
integer :: m ! zero-based offset in S
integer :: i ! one-based offset in W and T
integer, dimension(len(W)) :: T ! KMP table
call kmp_table(W, T)
i = 1
m = 0
do while (m + i <= len(S))
if (W(i:i) == S(m + i:m + i)) then
if (i == len(W)) then
res = m + 1
return
end if
i = i + 1
else
if (T(i) > 0) then
m = m + i - T(i)
i = T(i)
else
i = 1
m = m + 1
end if
end if
end do
res = 0
end function
(The index m is zero-based here, because t is only ever used in conjunction with i in S(m + i:m + i). Adding two one-based indices will yield an offset of one, whereas keeping m zero-based makes this a neutral addition. m is a local variable that isn't exposed to code from the outside.)
Alternatively, you could make your Fortran arrays zero-based by specifying a lower bound of zero for your string and array. That will clash with the useful character(*) notation, though, which always uses one-based indexing. In my opinion, it is better to think about the whole algorithm in the typical one-based indexing scheme of Fortran.
this site isn't really a debugging site. Normally I would suggest you have a look at how to debug code. It didn't take me very long to go through your code with a pen and paper and verify that that is indeed the table it produces.
Still, here are a few pointers:
The C code compares x[i] and x[j], but you compare x[i] and x[i+j] in your Fortran code, more or less.
Integer arrays usually also start at index 1 in Fortran. So just like adding one to the index in the x String, you also need to add 1 every time you access T anywhere.
I'm trying to get the exact equivalent (not functional) of this vb.net code in F#:
Function FastPow(ByVal num As Double, ByVal exp As Integer) As Double
Dim res As Double = 1
If exp < 1 Then
If exp = 0 Then Return res
exp = -exp
num = 1 / num
End If
Do While exp > 1
If exp Mod 2 = 1 Then
res = res * num
num = num * num
exp = exp >> 1
Loop
Return res * num
End Function
I wrote this:
let FastPow num exp =
let mutable ex = exp
let mutable res = 1
let mutable n = num
if ex < 1 then
if ex = 0 then res
ex <- -ex
n <- 1 / n
while ex > 1 do
if (ex % 2 = 1) then
res <- res * n
n <- n * n
exp >>> 1
res * n
but in the line "if ex = 0 then res" at res I got an error:
"This expression has type int but is here used with type unit".
I cannot understand why it gives me that error.
Edit: i actually got a warning as well:
"This expression should have type 'unit', but has type 'int'."
at "if (ex % 2 = 1) then"
In F#, a function's return value is the last expression evaluated in the function. So, lets focus on the following:
if ex < 1 then
if ex = 0 then res (* <--- this is not an early return *)
ex <- -ex (* <--- F# evaluates this code after the *)
n <- 1 / n (* if statement *)
Additionally, if statements have return values, which also happens to be the last value executed in the if statement. If an if statement isn't the return value of a function, it should have the return type unit. Notice that variable assignment has a return type of unit.
We need to rewrite your code to accomodate your early return, so we can do this:
let FastPow2 num exp =
if exp = 0 then 1
else
let mutable ex = exp
let mutable res = 1
let mutable n = num
if ex < 1 then
ex <- -ex
n <- 1 / n
while ex > 1 do
if (ex % 2 = 1) then (* still have a bug here *)
res <- res * n
n <- n * n
exp >>> 1 (* <--- this is not a variable assignment *)
res * n
We still have a bug, although I think F# is reporting the error in the wrong place. The expression exp >>> 1 returns an int, it does not assign any variables, so its not equivalent to your original C# code. I think you meant to use the ex variable instead. We can fix your code as follows:
let FastPow2 num exp =
if exp = 0 then 1
else
let mutable ex = exp
let mutable res = 1
let mutable n = num
if ex < 1 then
ex <- -ex
n <- 1 / n
while ex > 1 do
if (ex % 2 = 1) then
res <- res * n
n <- n * n
ex <- ex >>> 1
res * n
Now your function is fixed, but its really really ugly. Lets convert it to more idiomatic F#. You can replace the if statement with pattern matching, and replace the while loop with recursion:
let FastPow2 num exp =
match exp with
| 0 -> 1
| _ ->
let rec loop ex res n =
if ex > 1 then
let newRes = if ex % 2 = 1 then res * n else res
loop (ex >>> 1) newRes (n * n)
else res * n
let ex, n = if exp < 1 then (-exp, 1 / num) else (exp, num)
loop ex 1 n
Much better! Theres still some more room to beautify this function, but you get the idea :)
The problem is for an if statment to resolve to a value rather than unit, you need both the "then" part and the "else" part, both of which resolve to the same type.
For example:
let a = if true then 1;;
Will generate the same error - expression has type int but used with type unit.
However:
let a = if true then 1 else 0;;
Will evaluate to int without an error.
This is about as close as you can get, as others have already said you can't jump out of the middle of a functional and there's one place were you don't update a variable (at the bottom of the while).
let FastPow num exp =
let mutable exp = exp
let mutable res = 1
let mutable n = num
match exp with
| O -> n <- num
| _ when exp < 1 ->
exp <- -exp
n <- 1 / n
| _ ->
while exp > 1 do
if (exp % 2 = 1) then
res <- res * n
n <- n * n
exp <- exp >>> 1
res * n
I could be more beautiful if it was written more functionally.
It means that after then there should be some expression, but you have integer value. You cannot jump out from the middle of the function.
Edit
"If" didn't work because of
ex >>> 1
should be
ex <- ex >>> 1
Here's code that works:
let FastPow num exp =
let calcExp num exp =
let mutable res = 1.0
let mutable n = num
let mutable ex = exp
while ex > 1 do
if ((ex % 2) = 1) then
res <- res * n
n <- n * n
ex <- ex >>> 1
res * n
match exp with
| ex when ex = 0 -> 1.0
| ex when ex < 0 -> calcExp (1.0/num) -exp
| _ -> calcExp num exp
I just take out calculation as separate function, and at the end there is checking for arguments
Thanks for the answers. This is the current non-functional version.
let FastPow num exp =
let mutable ex = exp
let mutable res = 1.0
let mutable n = num
if ex = 0 then 1.0
else
if ex < 1 then
ex <- -ex
n <- 1.0 / n
while ex > 1 do
if (ex % 2 = 1) then res <- res * n
n <- n * n
ex <- ex >>> 1
res * n
Now that I have a working version I will try to make it more functional but that's outside the scope of this question.
EDIT: I got better results that I expected so I will post the recursive version optimized for speed (slightly faster than the iterative version and about 10% faster than the C# iterative version (!!!) in my computer):
let rec loop res num exp =
if exp = 0 then res
elif (exp % 2) = 1 then loop (res * num) (num * num) (exp / 2)
else loop res (num * num) (exp / 2)
let FP num exp =
let n = if exp < 0 then 1.0 / num else num
loop 1.0 n (Math.Abs(exp))