{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# OPTIONS_GHC -fspec-constr-count=24 #-}
{-# OPTIONS_GHC -Wno-incomplete-uni-patterns #-}
module Math.NumberTheory.Primes.Counting.Impl
( primeCount
, primeCountMaxArg
, nthPrime
) where
import Math.NumberTheory.Primes.Sieve.Eratosthenes
(PrimeSieve(..), primeList, primeSieve, psieveFrom, sieveTo, sieveBits, sieveRange)
import Math.NumberTheory.Primes.Sieve.Indexing (toPrim, idxPr)
import Math.NumberTheory.Primes.Counting.Approximate (nthPrimeApprox, approxPrimeCount)
import Math.NumberTheory.Primes.Types
import Math.NumberTheory.Roots
import Math.NumberTheory.Utils.FromIntegral
import Control.Monad.ST
import Data.Array.Base
import Data.Array.ST
import Data.Bits
import Data.Int
import Unsafe.Coerce
primeCountMaxArg :: Integer
primeCountMaxArg :: Integer
primeCountMaxArg = Integer
8000000000000000000
primeCount :: Integer -> Integer
primeCount :: Integer -> Integer
primeCount Integer
n
| Integer
n forall a. Ord a => a -> a -> Bool
> Integer
primeCountMaxArg = forall a. HasCallStack => [Char] -> a
error forall a b. (a -> b) -> a -> b
$ [Char]
"primeCount: can't handle bound " forall a. [a] -> [a] -> [a]
++ forall a. Show a => a -> [Char]
show Integer
n
| Integer
n forall a. Ord a => a -> a -> Bool
< Integer
2 = Integer
0
| Integer
n forall a. Ord a => a -> a -> Bool
< Integer
1000 = Int -> Integer
intToInteger forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (t :: * -> *) a. Foldable t => t a -> Int
length forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. (a -> Bool) -> [a] -> [a]
takeWhile (forall a. Ord a => a -> a -> Bool
<= Integer
n) forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b. (a -> b) -> [a] -> [b]
map forall a. Prime a -> a
unPrime forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. Integral a => PrimeSieve -> [Prime a]
primeList forall b c a. (b -> c) -> (a -> b) -> a -> c
. Integer -> PrimeSieve
primeSieve forall a b. (a -> b) -> a -> b
$ forall a. Ord a => a -> a -> a
max Integer
242 Integer
n
| Integer
n forall a. Ord a => a -> a -> Bool
< Integer
30000 = forall a. (forall s. ST s a) -> a
runST forall a b. (a -> b) -> a -> b
$ do
STUArray s Int Bool
ba <- forall s. Integer -> ST s (STUArray s Int Bool)
sieveTo Integer
n
(Int
s,Int
e) <- forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> m (i, i)
getBounds STUArray s Int Bool
ba
Int
ct <- forall s. Int -> Int -> STUArray s Int Bool -> ST s Int
countFromTo Int
s Int
e STUArray s Int Bool
ba
forall (m :: * -> *) a. Monad m => a -> m a
return (Int -> Integer
intToInteger forall a b. (a -> b) -> a -> b
$ Int
ctforall a. Num a => a -> a -> a
+Int
3)
| Bool
otherwise =
let !ub :: Int64
ub = Int64 -> Int64
cop forall a b. (a -> b) -> a -> b
$ forall a. Num a => Integer -> a
fromInteger Integer
n
!sr :: Int64
sr = forall a. Integral a => a -> a
integerSquareRoot Int64
ub
!cr :: Int64
cr = forall a. Integral a => a -> a
nxtEnd forall a b. (a -> b) -> a -> b
$ forall a. Integral a => a -> a
integerCubeRoot Int64
ub forall a. Num a => a -> a -> a
+ Int64
15
nxtEnd :: a -> a
nxtEnd a
k = a
k forall a. Num a => a -> a -> a
- (a
k forall a. Integral a => a -> a -> a
`rem` a
30) forall a. Num a => a -> a -> a
+ a
31
!phn1 :: Integer
phn1 = Int64 -> Int64 -> Integer
calc Int64
ub Int64
cr
!cs :: Int64
cs = Int64
crforall a. Num a => a -> a -> a
+Int64
6
!pdf :: Integer
pdf = Int64 -> Int64 -> Int64 -> Integer
sieveCount Int64
ub Int64
cs Int64
sr
in Integer
phn1 forall a. Num a => a -> a -> a
- Integer
pdf
nthPrime :: Int -> Prime Integer
nthPrime :: Int -> Prime Integer
nthPrime Int
1 = forall a. a -> Prime a
Prime Integer
2
nthPrime Int
2 = forall a. a -> Prime a
Prime Integer
3
nthPrime Int
3 = forall a. a -> Prime a
Prime Integer
5
nthPrime Int
4 = forall a. a -> Prime a
Prime Integer
7
nthPrime Int
5 = forall a. a -> Prime a
Prime Integer
11
nthPrime Int
6 = forall a. a -> Prime a
Prime Integer
13
nthPrime Int
n
| Int
n forall a. Ord a => a -> a -> Bool
< Int
1
= forall a. HasCallStack => [Char] -> a
error [Char]
"Prime indexing starts at 1"
| Int
n forall a. Ord a => a -> a -> Bool
< Int
200000
= forall a. a -> Prime a
Prime forall a b. (a -> b) -> a -> b
$ Int -> [PrimeSieve] -> Integer
countToNth (Int
n forall a. Num a => a -> a -> a
- Int
3) [Integer -> PrimeSieve
primeSieve (Integer
p0 forall a. Num a => a -> a -> a
+ Integer
p0 forall a. Integral a => a -> a -> a
`quot` Integer
32 forall a. Num a => a -> a -> a
+ Integer
37)]
| Integer
p0 forall a. Ord a => a -> a -> Bool
> forall a. Integral a => a -> Integer
toInteger (forall a. Bounded a => a
maxBound :: Int)
= forall a. HasCallStack => [Char] -> a
error forall a b. (a -> b) -> a -> b
$ [Char]
"nthPrime: index " forall a. [a] -> [a] -> [a]
++ forall a. Show a => a -> [Char]
show Int
n forall a. [a] -> [a] -> [a]
++ [Char]
" is too large to handle"
| Int
miss forall a. Ord a => a -> a -> Bool
> Int
0
= forall a. a -> Prime a
Prime forall a b. (a -> b) -> a -> b
$ Int -> Int -> Int -> Integer
tooLow Int
n (forall a. Num a => Integer -> a
fromInteger Integer
p0) Int
miss
| Bool
otherwise
= forall a. a -> Prime a
Prime forall a b. (a -> b) -> a -> b
$ Int -> Int -> Int -> Integer
tooHigh Int
n (forall a. Num a => Integer -> a
fromInteger Integer
p0) (forall a. Num a => a -> a
negate Int
miss)
where
p0 :: Integer
p0 = Integer -> Integer
nthPrimeApprox (forall a. Integral a => a -> Integer
toInteger Int
n)
miss :: Int
miss = Int
n forall a. Num a => a -> a -> a
- forall a. Num a => Integer -> a
fromInteger (Integer -> Integer
primeCount Integer
p0)
tooLow :: Int -> Int -> Int -> Integer
tooLow :: Int -> Int -> Int -> Integer
tooLow Int
n Int
p0 Int
shortage
| Integer
p1 forall a. Ord a => a -> a -> Bool
> forall a. Integral a => a -> Integer
toInteger (forall a. Bounded a => a
maxBound :: Int)
= forall a. HasCallStack => [Char] -> a
error forall a b. (a -> b) -> a -> b
$ [Char]
"nthPrime: index " forall a. [a] -> [a] -> [a]
++ forall a. Show a => a -> [Char]
show Int
n forall a. [a] -> [a] -> [a]
++ [Char]
" is too large to handle"
| Bool
goodEnough
= Int -> Int -> Integer
lowSieve Int
p0 Int
shortage
| Int
c1 forall a. Ord a => a -> a -> Bool
< Int
n
= Int -> Int -> Integer
lowSieve (forall a. Num a => Integer -> a
fromInteger Integer
p1) (Int
nforall a. Num a => a -> a -> a
-Int
c1)
| Bool
otherwise
= Int -> Int -> Integer
lowSieve Int
p0 Int
shortage
where
gap :: Integer
gap = forall a b. (RealFrac a, Integral b) => a -> b
truncate (forall a. Floating a => a -> a
log (Int -> Double
intToDouble Int
p0 :: Double))
est :: Integer
est = forall a. Integral a => a -> Integer
toInteger Int
shortage forall a. Num a => a -> a -> a
* Integer
gap
p1 :: Integer
p1 = forall a. Integral a => a -> Integer
toInteger Int
p0 forall a. Num a => a -> a -> a
+ Integer
est
goodEnough :: Bool
goodEnough = Integer
3forall a. Num a => a -> a -> a
*Integer
estforall a. Num a => a -> a -> a
*Integer
estforall a. Num a => a -> a -> a
*Integer
est forall a. Ord a => a -> a -> Bool
< Integer
2forall a. Num a => a -> a -> a
*Integer
p1forall a. Num a => a -> a -> a
*Integer
p1
c1 :: Int
c1 = forall a. Num a => Integer -> a
fromInteger (Integer -> Integer
primeCount Integer
p1)
tooHigh :: Int -> Int -> Int -> Integer
tooHigh :: Int -> Int -> Int -> Integer
tooHigh Int
n Int
p0 Int
surplus
| Int
c forall a. Ord a => a -> a -> Bool
< Int
n
= Int -> Int -> Integer
lowSieve Int
b (Int
nforall a. Num a => a -> a -> a
-Int
c)
| Bool
otherwise
= Int -> Int -> Int -> Integer
tooHigh Int
n Int
b (Int
cforall a. Num a => a -> a -> a
-Int
n)
where
gap :: Int
gap = forall a b. (RealFrac a, Integral b) => a -> b
truncate (forall a. Floating a => a -> a
log (Int -> Double
intToDouble Int
p0 :: Double))
b :: Int
b = Int
p0 forall a. Num a => a -> a -> a
- (Int
surplus forall a. Num a => a -> a -> a
* Int
gap forall a. Num a => a -> a -> a
* Int
11) forall a. Integral a => a -> a -> a
`quot` Int
10
c :: Int
c = forall a. Num a => Integer -> a
fromInteger (Integer -> Integer
primeCount (forall a. Integral a => a -> Integer
toInteger Int
b))
lowSieve :: Int -> Int -> Integer
lowSieve :: Int -> Int -> Integer
lowSieve Int
a Int
miss = Int -> [PrimeSieve] -> Integer
countToNth (Int
missforall a. Num a => a -> a -> a
+Int
rep) [PrimeSieve]
psieves
where
strt :: Int
strt = Int
a forall a. Num a => a -> a -> a
+ Int
1 forall a. Num a => a -> a -> a
+ (Int
a forall a. Bits a => a -> a -> a
.&. Int
1)
psieves :: [PrimeSieve]
psieves@(PS Integer
vO UArray Int Bool
ba:[PrimeSieve]
_) = Integer -> [PrimeSieve]
psieveFrom (forall a. Integral a => a -> Integer
toInteger Int
strt)
rep :: Int
rep | Integer
o0 forall a. Ord a => a -> a -> Bool
< Integer
0 = Int
0
| Bool
otherwise = forall (t :: * -> *) a. (Foldable t, Num a) => t a -> a
sum [Int
1 | Int
i <- [Int
0 .. Int
r2], UArray Int Bool
ba forall (a :: * -> * -> *) e i.
(IArray a e, Ix i) =>
a i e -> Int -> e
`unsafeAt` Int
i]
where
o0 :: Integer
o0 = forall a. Integral a => a -> Integer
toInteger Int
strt forall a. Num a => a -> a -> a
- Integer
vO forall a. Num a => a -> a -> a
- Integer
9
r0 :: Int
r0 = forall a. Num a => Integer -> a
fromInteger Integer
o0 forall a. Integral a => a -> a -> a
`rem` Int
30
r1 :: Int
r1 = Int
r0 forall a. Integral a => a -> a -> a
`quot` Int
3
r2 :: Int
r2 = forall a. Ord a => a -> a -> a
min Int
7 (if Int
r1 forall a. Ord a => a -> a -> Bool
> Int
5 then Int
r1forall a. Num a => a -> a -> a
-Int
1 else Int
r1)
sieveCount :: Int64 -> Int64 -> Int64 -> Integer
sieveCount :: Int64 -> Int64 -> Int64 -> Integer
sieveCount Int64
ub Int64
cr Int64
sr = forall a. (forall s. ST s a) -> a
runST (forall s. Int64 -> Int64 -> Int64 -> ST s Integer
sieveCountST Int64
ub Int64
cr Int64
sr)
sieveCountST :: forall s. Int64 -> Int64 -> Int64 -> ST s Integer
sieveCountST :: forall s. Int64 -> Int64 -> Int64 -> ST s Integer
sieveCountST Int64
ub Int64
cr Int64
sr = do
let psieves :: [PrimeSieve]
psieves = Integer -> [PrimeSieve]
psieveFrom (Int64 -> Integer
int64ToInteger Int64
cr)
pisr :: Int64
pisr = forall a. Integral a => a -> a
approxPrimeCount Int64
sr
picr :: Int64
picr = forall a. Integral a => a -> a
approxPrimeCount Int64
cr
diff :: Int64
diff = Int64
pisr forall a. Num a => a -> a -> a
- Int64
picr
size :: Int
size = Int64 -> Int
int64ToInt (Int64
diff forall a. Num a => a -> a -> a
+ Int64
diff forall a. Integral a => a -> a -> a
`quot` Int64
50) forall a. Num a => a -> a -> a
+ Int
30
STUArray s Int Int64
store <- forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
(i, i) -> m (a i e)
unsafeNewArray_ (Int
0,Int
sizeforall a. Num a => a -> a -> a
-Int
1) :: ST s (STUArray s Int Int64)
let feed :: Int64 -> Int -> Int -> UArray Int Bool -> [PrimeSieve] -> ST s Integer
feed :: Int64
-> Int -> Int -> UArray Int Bool -> [PrimeSieve] -> ST s Integer
feed Int64
voff !Int
wi !Int
ri UArray Int Bool
uar [PrimeSieve]
sves
| Int
ri forall a. Eq a => a -> a -> Bool
== Int
sieveBits = case [PrimeSieve]
sves of
(PS Integer
vO UArray Int Bool
ba : [PrimeSieve]
more) -> Int64
-> Int -> Int -> UArray Int Bool -> [PrimeSieve] -> ST s Integer
feed (forall a. Num a => Integer -> a
fromInteger Integer
vO) Int
wi Int
0 UArray Int Bool
ba [PrimeSieve]
more
[PrimeSieve]
_ -> forall a. HasCallStack => [Char] -> a
error [Char]
"prime stream ended prematurely"
| Int64
pval forall a. Ord a => a -> a -> Bool
> Int64
sr = do
STUArray s Int Bool
stu <- forall i (a :: * -> * -> *) e (b :: * -> * -> *) (m :: * -> *).
(Ix i, IArray a e, MArray b e m) =>
a i e -> m (b i e)
unsafeThaw UArray Int Bool
uar
Integer
-> Integer
-> Int64
-> Int
-> Int
-> STUArray s Int Bool
-> [PrimeSieve]
-> ST s Integer
eat Integer
0 Integer
0 Int64
voff (Int
wiforall a. Num a => a -> a -> a
-Int
1) Int
ri STUArray s Int Bool
stu [PrimeSieve]
sves
| UArray Int Bool
uar forall (a :: * -> * -> *) e i.
(IArray a e, Ix i) =>
a i e -> Int -> e
`unsafeAt` Int
ri = do
forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> e -> m ()
unsafeWrite STUArray s Int Int64
store Int
wi (Int64
ub forall a. Integral a => a -> a -> a
`quot` Int64
pval)
Int64
-> Int -> Int -> UArray Int Bool -> [PrimeSieve] -> ST s Integer
feed Int64
voff (Int
wiforall a. Num a => a -> a -> a
+Int
1) (Int
riforall a. Num a => a -> a -> a
+Int
1) UArray Int Bool
uar [PrimeSieve]
sves
| Bool
otherwise = Int64
-> Int -> Int -> UArray Int Bool -> [PrimeSieve] -> ST s Integer
feed Int64
voff Int
wi (Int
riforall a. Num a => a -> a -> a
+Int
1) UArray Int Bool
uar [PrimeSieve]
sves
where
pval :: Int64
pval = Int64
voff forall a. Num a => a -> a -> a
+ forall a. Num a => Int -> a
toPrim Int
ri
eat :: Integer -> Integer -> Int64 -> Int -> Int -> STUArray s Int Bool -> [PrimeSieve] -> ST s Integer
eat :: Integer
-> Integer
-> Int64
-> Int
-> Int
-> STUArray s Int Bool
-> [PrimeSieve]
-> ST s Integer
eat !Integer
acc !Integer
btw Int64
voff !Int
wi !Int
si STUArray s Int Bool
stu [PrimeSieve]
sves
| Int
si forall a. Eq a => a -> a -> Bool
== Int
sieveBits =
case [PrimeSieve]
sves of
[] -> forall a. HasCallStack => [Char] -> a
error [Char]
"Premature end of prime stream"
(PS Integer
vO UArray Int Bool
ba : [PrimeSieve]
more) -> do
STUArray s Int Bool
nstu <- forall i (a :: * -> * -> *) e (b :: * -> * -> *) (m :: * -> *).
(Ix i, IArray a e, MArray b e m) =>
a i e -> m (b i e)
unsafeThaw UArray Int Bool
ba
Integer
-> Integer
-> Int64
-> Int
-> Int
-> STUArray s Int Bool
-> [PrimeSieve]
-> ST s Integer
eat Integer
acc Integer
btw (forall a. Num a => Integer -> a
fromInteger Integer
vO) Int
wi Int
0 STUArray s Int Bool
nstu [PrimeSieve]
more
| Int
wi forall a. Ord a => a -> a -> Bool
< Int
0 = forall (m :: * -> *) a. Monad m => a -> m a
return Integer
acc
| Bool
otherwise = do
Int64
qb <- forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> m e
unsafeRead STUArray s Int Int64
store Int
wi
let dist :: Int64
dist = Int64
qb forall a. Num a => a -> a -> a
- Int64
voff forall a. Num a => a -> a -> a
- Int64
7
if Int64
dist forall a. Ord a => a -> a -> Bool
< Int -> Int64
intToInt64 Int
sieveRange
then do
let (Int
b,Int
j) = forall a. Integral a => a -> (Int, Int)
idxPr (Int64
distforall a. Num a => a -> a -> a
+Int64
7)
!li :: Int
li = (Int
b forall a. Bits a => a -> Int -> a
`shiftL` Int
3) forall a. Bits a => a -> a -> a
.|. Int
j
Int
new <- if Int
li forall a. Ord a => a -> a -> Bool
< Int
si then forall (m :: * -> *) a. Monad m => a -> m a
return Int
0 else forall s. Int -> Int -> STUArray s Int Bool -> ST s Int
countFromTo Int
si Int
li STUArray s Int Bool
stu
let nbtw :: Integer
nbtw = Integer
btw forall a. Num a => a -> a -> a
+ Int -> Integer
intToInteger Int
new forall a. Num a => a -> a -> a
+ Integer
1
Integer
-> Integer
-> Int64
-> Int
-> Int
-> STUArray s Int Bool
-> [PrimeSieve]
-> ST s Integer
eat (Integer
accforall a. Num a => a -> a -> a
+Integer
nbtw) Integer
nbtw Int64
voff (Int
wiforall a. Num a => a -> a -> a
-Int
1) (Int
liforall a. Num a => a -> a -> a
+Int
1) STUArray s Int Bool
stu [PrimeSieve]
sves
else do
let (Int64
cpl,Int64
fds) = Int64
dist forall a. Integral a => a -> a -> (a, a)
`quotRem` Int -> Int64
intToInt64 Int
sieveRange
(Int
b,Int
j) = forall a. Integral a => a -> (Int, Int)
idxPr (Int64
fdsforall a. Num a => a -> a -> a
+Int64
7)
!li :: Int
li = (Int
b forall a. Bits a => a -> Int -> a
`shiftL` Int
3) forall a. Bits a => a -> a -> a
.|. Int
j
ctLoop :: Integer -> t -> [PrimeSieve] -> ST s Integer
ctLoop !Integer
lac t
0 (PS Integer
vO UArray Int Bool
ba : [PrimeSieve]
more) = do
STUArray s Int Bool
nstu <- forall i (a :: * -> * -> *) e (b :: * -> * -> *) (m :: * -> *).
(Ix i, IArray a e, MArray b e m) =>
a i e -> m (b i e)
unsafeThaw UArray Int Bool
ba
Int
new <- forall s. Int -> Int -> STUArray s Int Bool -> ST s Int
countFromTo Int
0 Int
li STUArray s Int Bool
nstu
let nbtw :: Integer
nbtw = Integer
btw forall a. Num a => a -> a -> a
+ Integer
lac forall a. Num a => a -> a -> a
+ Integer
1 forall a. Num a => a -> a -> a
+ Int -> Integer
intToInteger Int
new
Integer
-> Integer
-> Int64
-> Int
-> Int
-> STUArray s Int Bool
-> [PrimeSieve]
-> ST s Integer
eat (Integer
accforall a. Num a => a -> a -> a
+Integer
nbtw) Integer
nbtw (Integer -> Int64
integerToInt64 Integer
vO) (Int
wiforall a. Num a => a -> a -> a
-Int
1) (Int
liforall a. Num a => a -> a -> a
+Int
1) STUArray s Int Bool
nstu [PrimeSieve]
more
ctLoop Integer
lac t
s (PrimeSieve
ps : [PrimeSieve]
more) = do
let !new :: Int
new = PrimeSieve -> Int
countAll PrimeSieve
ps
Integer -> t -> [PrimeSieve] -> ST s Integer
ctLoop (Integer
lac forall a. Num a => a -> a -> a
+ Int -> Integer
intToInteger Int
new) (t
sforall a. Num a => a -> a -> a
-t
1) [PrimeSieve]
more
ctLoop Integer
_ t
_ [] = forall a. HasCallStack => [Char] -> a
error [Char]
"Primes ended"
Int
new <- forall s. Int -> Int -> STUArray s Int Bool -> ST s Int
countFromTo Int
si (Int
sieveBitsforall a. Num a => a -> a -> a
-Int
1) STUArray s Int Bool
stu
forall {t}.
(Eq t, Num t) =>
Integer -> t -> [PrimeSieve] -> ST s Integer
ctLoop (Int -> Integer
intToInteger Int
new) (Int64
cplforall a. Num a => a -> a -> a
-Int64
1) [PrimeSieve]
sves
case [PrimeSieve]
psieves of
(PS Integer
vO UArray Int Bool
ba : [PrimeSieve]
more) -> Int64
-> Int -> Int -> UArray Int Bool -> [PrimeSieve] -> ST s Integer
feed (forall a. Num a => Integer -> a
fromInteger Integer
vO) Int
0 Int
0 UArray Int Bool
ba [PrimeSieve]
more
[PrimeSieve]
_ -> forall a. HasCallStack => [Char] -> a
error [Char]
"No primes sieved"
calc :: Int64 -> Int64 -> Integer
calc :: Int64 -> Int64 -> Integer
calc Int64
lim Int64
plim = forall a. (forall s. ST s a) -> a
runST (forall s. Int64 -> Int64 -> ST s Integer
calcST Int64
lim Int64
plim)
calcST :: forall s. Int64 -> Int64 -> ST s Integer
calcST :: forall s. Int64 -> Int64 -> ST s Integer
calcST Int64
lim Int64
plim = do
!STUArray s Int Bool
parr <- forall s. Integer -> ST s (STUArray s Int Bool)
sieveTo (Int64 -> Integer
int64ToInteger Int64
plim)
(Int
plo,Int
phi) <- forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> m (i, i)
getBounds STUArray s Int Bool
parr
!Int
pct <- forall s. Int -> Int -> STUArray s Int Bool -> ST s Int
countFromTo Int
plo Int
phi STUArray s Int Bool
parr
!STUArray s Int Int64
ar1 <- forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
(i, i) -> m (a i e)
unsafeNewArray_ (Int
0,Int
endforall a. Num a => a -> a -> a
-Int
1)
forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> e -> m ()
unsafeWrite STUArray s Int Int64
ar1 Int
0 Int64
lim
forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> e -> m ()
unsafeWrite STUArray s Int Int64
ar1 Int
1 Int64
1
!STUArray s Int Int64
ar2 <- forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
(i, i) -> m (a i e)
unsafeNewArray_ (Int
0,Int
endforall a. Num a => a -> a -> a
-Int
1)
let go :: Int -> Int -> STUArray s Int Int64 -> STUArray s Int Int64 -> ST s Integer
go :: Int
-> Int
-> STUArray s Int Int64
-> STUArray s Int Int64
-> ST s Integer
go Int
cap Int
pix STUArray s Int Int64
old STUArray s Int Int64
new
| Int
pix forall a. Eq a => a -> a -> Bool
== Int
2 = Int -> STUArray s Int Int64 -> ST s Integer
coll Int
cap STUArray s Int Int64
old
| Bool
otherwise = do
Bool
isp <- forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> m e
unsafeRead STUArray s Int Bool
parr Int
pix
if Bool
isp
then do
let !n :: Int64
n = forall a. Num a => Integer -> a
fromInteger (forall a. Num a => Int -> a
toPrim Int
pix)
!Int
ncap <- forall s.
Int
-> Int64
-> STUArray s Int Int64
-> STUArray s Int Int64
-> ST s Int
treat Int
cap Int64
n STUArray s Int Int64
old STUArray s Int Int64
new
Int
-> Int
-> STUArray s Int Int64
-> STUArray s Int Int64
-> ST s Integer
go Int
ncap (Int
pixforall a. Num a => a -> a -> a
-Int
1) STUArray s Int Int64
new STUArray s Int Int64
old
else Int
-> Int
-> STUArray s Int Int64
-> STUArray s Int Int64
-> ST s Integer
go Int
cap (Int
pixforall a. Num a => a -> a -> a
-Int
1) STUArray s Int Int64
old STUArray s Int Int64
new
coll :: Int -> STUArray s Int Int64 -> ST s Integer
coll :: Int -> STUArray s Int Int64 -> ST s Integer
coll Int
stop STUArray s Int Int64
ar =
let cgo :: Integer -> Int -> m Integer
cgo !Integer
acc Int
i
| Int
i forall a. Ord a => a -> a -> Bool
< Int
stop = do
!Int64
k <- forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> m e
unsafeRead STUArray s Int Int64
ar Int
i
!Int64
v <- forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> m e
unsafeRead STUArray s Int Int64
ar (Int
iforall a. Num a => a -> a -> a
+Int
1)
Integer -> Int -> m Integer
cgo (Integer
acc forall a. Num a => a -> a -> a
+ Int64 -> Integer
int64ToInteger Int64
vforall a. Num a => a -> a -> a
*Int64 -> Integer
cp6 Int64
k) (Int
iforall a. Num a => a -> a -> a
+Int
2)
| Bool
otherwise = forall (m :: * -> *) a. Monad m => a -> m a
return (Integer
accforall a. Num a => a -> a -> a
+Int -> Integer
intToInteger Int
pctforall a. Num a => a -> a -> a
+Integer
2)
in forall {m :: * -> *}.
MArray (STUArray s) Int64 m =>
Integer -> Int -> m Integer
cgo Integer
0 Int
0
Int
-> Int
-> STUArray s Int Int64
-> STUArray s Int Int64
-> ST s Integer
go Int
2 Int
start STUArray s Int Int64
ar1 STUArray s Int Int64
ar2
where
(Int
bt,Int
ri) = forall a. Integral a => a -> (Int, Int)
idxPr Int64
plim
!start :: Int
start = Int
8forall a. Num a => a -> a -> a
*Int
bt forall a. Num a => a -> a -> a
+ Int
ri
!size :: Int
size = Int64 -> Int
int64ToInt forall a b. (a -> b) -> a -> b
$ forall a. Integral a => a -> a
integerSquareRoot Int64
lim forall a. Integral a => a -> a -> a
`quot` Int64
4
!end :: Int
end = Int
2forall a. Num a => a -> a -> a
*Int
size
treat :: Int -> Int64 -> STUArray s Int Int64 -> STUArray s Int Int64 -> ST s Int
treat :: forall s.
Int
-> Int64
-> STUArray s Int Int64
-> STUArray s Int Int64
-> ST s Int
treat Int
end Int64
n STUArray s Int Int64
old STUArray s Int Int64
new = do
Int
qi0 <- forall s. Int64 -> Int -> Int -> STUArray s Int Int64 -> ST s Int
locate Int64
n Int
0 (Int
end forall a. Integral a => a -> a -> a
`quot` Int
2 forall a. Num a => a -> a -> a
- Int
1) STUArray s Int Int64
old
let collect :: Int64 -> Int64 -> Int -> m (Int64, Int)
collect Int64
stop !Int64
acc Int
ix
| Int
ix forall a. Ord a => a -> a -> Bool
< Int
end = do
!Int64
k <- forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> m e
unsafeRead STUArray s Int Int64
old Int
ix
if Int64
k forall a. Ord a => a -> a -> Bool
< Int64
stop
then do
Int64
v <- forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> m e
unsafeRead STUArray s Int Int64
old (Int
ixforall a. Num a => a -> a -> a
+Int
1)
Int64 -> Int64 -> Int -> m (Int64, Int)
collect Int64
stop (Int64
accforall a. Num a => a -> a -> a
-Int64
v) (Int
ixforall a. Num a => a -> a -> a
+Int
2)
else forall (m :: * -> *) a. Monad m => a -> m a
return (Int64
acc,Int
ix)
| Bool
otherwise = forall (m :: * -> *) a. Monad m => a -> m a
return (Int64
acc,Int
ix)
goTreat :: Int -> Int -> Int -> ST s Int
goTreat !Int
wi !Int
ci Int
qi
| Int
qi forall a. Ord a => a -> a -> Bool
< Int
end = do
!Int64
key <- forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> m e
unsafeRead STUArray s Int Int64
old Int
qi
!Int64
val <- forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> m e
unsafeRead STUArray s Int Int64
old (Int
qiforall a. Num a => a -> a -> a
+Int
1)
let !q0 :: Int64
q0 = Int64
key forall a. Integral a => a -> a -> a
`quot` Int64
n
!r0 :: Int
r0 = Int64 -> Int
int64ToInt (Int64
q0 forall a. Integral a => a -> a -> a
`rem` Int64
30030)
!nkey :: Int64
nkey = Int64
q0 forall a. Num a => a -> a -> a
- Int8 -> Int64
int8ToInt64 (UArray Int Int8
cpDfAr forall (a :: * -> * -> *) e i.
(IArray a e, Ix i) =>
a i e -> Int -> e
`unsafeAt` Int
r0)
nk0 :: Int64
nk0 = Int64
q0 forall a. Num a => a -> a -> a
+ Int8 -> Int64
int8ToInt64 (UArray Int Int8
cpGpAr forall (a :: * -> * -> *) e i.
(IArray a e, Ix i) =>
a i e -> Int -> e
`unsafeAt` (Int
r0forall a. Num a => a -> a -> a
+Int
1) forall a. Num a => a -> a -> a
+ Int8
1)
!nlim :: Int64
nlim = Int64
nforall a. Num a => a -> a -> a
*Int64
nk0
(Int
wi1,Int
ci1) <- forall s.
Int
-> Int64
-> STUArray s Int Int64
-> Int
-> STUArray s Int Int64
-> Int
-> ST s (Int, Int)
copyTo Int
end Int64
nkey STUArray s Int Int64
old Int
ci STUArray s Int Int64
new Int
wi
Int64
ckey <- forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> m e
unsafeRead STUArray s Int Int64
old Int
ci1
(!Int64
acc, !Int
ci2) <- if Int64
ckey forall a. Eq a => a -> a -> Bool
== Int64
nkey
then do
!Int64
ov <- forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> m e
unsafeRead STUArray s Int Int64
old (Int
ci1forall a. Num a => a -> a -> a
+Int
1)
forall (m :: * -> *) a. Monad m => a -> m a
return (Int64
ovforall a. Num a => a -> a -> a
-Int64
val,Int
ci1forall a. Num a => a -> a -> a
+Int
2)
else forall (m :: * -> *) a. Monad m => a -> m a
return (-Int64
val,Int
ci1)
(!Int64
tot, !Int
nqi) <- forall {m :: * -> *}.
MArray (STUArray s) Int64 m =>
Int64 -> Int64 -> Int -> m (Int64, Int)
collect Int64
nlim Int64
acc (Int
qiforall a. Num a => a -> a -> a
+Int
2)
forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> e -> m ()
unsafeWrite STUArray s Int Int64
new Int
wi1 Int64
nkey
forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> e -> m ()
unsafeWrite STUArray s Int Int64
new (Int
wi1forall a. Num a => a -> a -> a
+Int
1) Int64
tot
Int -> Int -> Int -> ST s Int
goTreat (Int
wi1forall a. Num a => a -> a -> a
+Int
2) Int
ci2 Int
nqi
| Bool
otherwise = forall s.
Int
-> STUArray s Int Int64
-> Int
-> STUArray s Int Int64
-> Int
-> ST s Int
copyRem Int
end STUArray s Int Int64
old Int
ci STUArray s Int Int64
new Int
wi
Int -> Int -> Int -> ST s Int
goTreat Int
0 Int
0 Int
qi0
locate :: Int64 -> Int -> Int -> STUArray s Int Int64 -> ST s Int
locate :: forall s. Int64 -> Int -> Int -> STUArray s Int Int64 -> ST s Int
locate Int64
p Int
low Int
high STUArray s Int Int64
arr = do
let go :: Int -> Int -> m Int
go Int
lo Int
hi
| Int
lo forall a. Ord a => a -> a -> Bool
< Int
hi = do
let !md :: Int
md = (Int
loforall a. Num a => a -> a -> a
+Int
hi) forall a. Integral a => a -> a -> a
`quot` Int
2
Int64
v <- forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> m e
unsafeRead STUArray s Int Int64
arr (Int
2forall a. Num a => a -> a -> a
*Int
md)
case forall a. Ord a => a -> a -> Ordering
compare Int64
p Int64
v of
Ordering
LT -> Int -> Int -> m Int
go Int
lo Int
md
Ordering
EQ -> forall (m :: * -> *) a. Monad m => a -> m a
return (Int
2forall a. Num a => a -> a -> a
*Int
md)
Ordering
GT -> Int -> Int -> m Int
go (Int
mdforall a. Num a => a -> a -> a
+Int
1) Int
hi
| Bool
otherwise = forall (m :: * -> *) a. Monad m => a -> m a
return (Int
2forall a. Num a => a -> a -> a
*Int
lo)
forall {m :: * -> *}.
MArray (STUArray s) Int64 m =>
Int -> Int -> m Int
go Int
low Int
high
{-# INLINE copyTo #-}
copyTo :: Int -> Int64 -> STUArray s Int Int64 -> Int
-> STUArray s Int Int64 -> Int -> ST s (Int,Int)
copyTo :: forall s.
Int
-> Int64
-> STUArray s Int Int64
-> Int
-> STUArray s Int Int64
-> Int
-> ST s (Int, Int)
copyTo Int
end Int64
lim STUArray s Int Int64
old Int
oi STUArray s Int Int64
new Int
ni = do
let go :: Int -> Int -> m (Int, Int)
go Int
ri Int
wi
| Int
ri forall a. Ord a => a -> a -> Bool
< Int
end = do
Int64
ok <- forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> m e
unsafeRead STUArray s Int Int64
old Int
ri
if Int64
ok forall a. Ord a => a -> a -> Bool
< Int64
lim
then do
!Int64
ov <- forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> m e
unsafeRead STUArray s Int Int64
old (Int
riforall a. Num a => a -> a -> a
+Int
1)
forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> e -> m ()
unsafeWrite STUArray s Int Int64
new Int
wi Int64
ok
forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> e -> m ()
unsafeWrite STUArray s Int Int64
new (Int
wiforall a. Num a => a -> a -> a
+Int
1) Int64
ov
Int -> Int -> m (Int, Int)
go (Int
riforall a. Num a => a -> a -> a
+Int
2) (Int
wiforall a. Num a => a -> a -> a
+Int
2)
else forall (m :: * -> *) a. Monad m => a -> m a
return (Int
wi,Int
ri)
| Bool
otherwise = forall (m :: * -> *) a. Monad m => a -> m a
return (Int
wi,Int
ri)
forall {m :: * -> *}.
MArray (STUArray s) Int64 m =>
Int -> Int -> m (Int, Int)
go Int
oi Int
ni
{-# INLINE copyRem #-}
copyRem :: Int -> STUArray s Int Int64 -> Int -> STUArray s Int Int64 -> Int -> ST s Int
copyRem :: forall s.
Int
-> STUArray s Int Int64
-> Int
-> STUArray s Int Int64
-> Int
-> ST s Int
copyRem Int
end STUArray s Int Int64
old Int
oi STUArray s Int Int64
new Int
ni = do
let go :: Int -> Int -> m Int
go Int
ri Int
wi
| Int
ri forall a. Ord a => a -> a -> Bool
< Int
end = do
forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> m e
unsafeRead STUArray s Int Int64
old Int
ri forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
>>= forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> e -> m ()
unsafeWrite STUArray s Int Int64
new Int
wi
Int -> Int -> m Int
go (Int
riforall a. Num a => a -> a -> a
+Int
1) (Int
wiforall a. Num a => a -> a -> a
+Int
1)
| Bool
otherwise = forall (m :: * -> *) a. Monad m => a -> m a
return Int
wi
forall {m :: * -> *}.
MArray (STUArray s) Int64 m =>
Int -> Int -> m Int
go Int
oi Int
ni
{-# INLINE cp6 #-}
cp6 :: Int64 -> Integer
cp6 :: Int64 -> Integer
cp6 Int64
k =
case Int64
k forall a. Integral a => a -> a -> (a, a)
`quotRem` Int64
30030 of
(Int64
q,Int64
r) -> Integer
5760forall a. Num a => a -> a -> a
*Int64 -> Integer
int64ToInteger Int64
q forall a. Num a => a -> a -> a
+
Int16 -> Integer
int16ToInteger (UArray Int Int16
cpCtAr forall (a :: * -> * -> *) e i.
(IArray a e, Ix i) =>
a i e -> Int -> e
`unsafeAt` Int64 -> Int
int64ToInt Int64
r)
cop :: Int64 -> Int64
cop :: Int64 -> Int64
cop Int64
m = Int64
m forall a. Num a => a -> a -> a
- Int8 -> Int64
int8ToInt64 (UArray Int Int8
cpDfAr forall (a :: * -> * -> *) e i.
(IArray a e, Ix i) =>
a i e -> Int -> e
`unsafeAt` Int64 -> Int
int64ToInt (Int64
m forall a. Integral a => a -> a -> a
`rem` Int64
30030))
cpCtAr :: UArray Int Int16
cpCtAr :: UArray Int Int16
cpCtAr = forall i e. (forall s. ST s (STUArray s i e)) -> UArray i e
runSTUArray forall a b. (a -> b) -> a -> b
$ do
STUArray s Int Int16
ar <- forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
(i, i) -> e -> m (a i e)
newArray (Int
0,Int
30029) Int16
1
let zilch :: Int -> Int -> m ()
zilch Int
s Int
i
| Int
i forall a. Ord a => a -> a -> Bool
< Int
30030 = forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> e -> m ()
unsafeWrite STUArray s Int Int16
ar Int
i Int16
0 forall (m :: * -> *) a b. Monad m => m a -> m b -> m b
>> Int -> Int -> m ()
zilch Int
s (Int
iforall a. Num a => a -> a -> a
+Int
s)
| Bool
otherwise = forall (m :: * -> *) a. Monad m => a -> m a
return ()
accumulate :: Int16 -> Int -> m (STUArray s Int Int16)
accumulate Int16
ct Int
i
| Int
i forall a. Ord a => a -> a -> Bool
< Int
30030 = do
Int16
v <- forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> m e
unsafeRead STUArray s Int Int16
ar Int
i
let !ct' :: Int16
ct' = Int16
ctforall a. Num a => a -> a -> a
+Int16
v
forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> e -> m ()
unsafeWrite STUArray s Int Int16
ar Int
i Int16
ct'
Int16 -> Int -> m (STUArray s Int Int16)
accumulate Int16
ct' (Int
iforall a. Num a => a -> a -> a
+Int
1)
| Bool
otherwise = forall (m :: * -> *) a. Monad m => a -> m a
return STUArray s Int Int16
ar
forall {m :: * -> *}.
MArray (STUArray s) Int16 m =>
Int -> Int -> m ()
zilch Int
2 Int
0
forall {m :: * -> *}.
MArray (STUArray s) Int16 m =>
Int -> Int -> m ()
zilch Int
6 Int
3
forall {m :: * -> *}.
MArray (STUArray s) Int16 m =>
Int -> Int -> m ()
zilch Int
10 Int
5
forall {m :: * -> *}.
MArray (STUArray s) Int16 m =>
Int -> Int -> m ()
zilch Int
14 Int
7
forall {m :: * -> *}.
MArray (STUArray s) Int16 m =>
Int -> Int -> m ()
zilch Int
22 Int
11
forall {m :: * -> *}.
MArray (STUArray s) Int16 m =>
Int -> Int -> m ()
zilch Int
26 Int
13
forall {m :: * -> *}.
MArray (STUArray s) Int16 m =>
Int16 -> Int -> m (STUArray s Int Int16)
accumulate Int16
1 Int
2
cpDfAr :: UArray Int Int8
cpDfAr :: UArray Int Int8
cpDfAr = forall i e. (forall s. ST s (STUArray s i e)) -> UArray i e
runSTUArray forall a b. (a -> b) -> a -> b
$ do
STUArray s Int Int8
ar <- forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
(i, i) -> e -> m (a i e)
newArray (Int
0,Int
30029) Int8
0
let note :: Int -> Int -> m ()
note Int
s Int
i
| Int
i forall a. Ord a => a -> a -> Bool
< Int
30029 = forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> e -> m ()
unsafeWrite STUArray s Int Int8
ar Int
i Int8
1 forall (m :: * -> *) a b. Monad m => m a -> m b -> m b
>> Int -> Int -> m ()
note Int
s (Int
iforall a. Num a => a -> a -> a
+Int
s)
| Bool
otherwise = forall (m :: * -> *) a. Monad m => a -> m a
return ()
accumulate :: Int8 -> Int -> m (STUArray s Int Int8)
accumulate Int8
d Int
i
| Int
i forall a. Ord a => a -> a -> Bool
< Int
30029 = do
Int8
v <- forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> m e
unsafeRead STUArray s Int Int8
ar Int
i
if Int8
v forall a. Eq a => a -> a -> Bool
== Int8
0
then Int8 -> Int -> m (STUArray s Int Int8)
accumulate Int8
2 (Int
iforall a. Num a => a -> a -> a
+Int
2)
else do forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> e -> m ()
unsafeWrite STUArray s Int Int8
ar Int
i Int8
d
Int8 -> Int -> m (STUArray s Int Int8)
accumulate (Int8
dforall a. Num a => a -> a -> a
+Int8
1) (Int
iforall a. Num a => a -> a -> a
+Int
1)
| Bool
otherwise = forall (m :: * -> *) a. Monad m => a -> m a
return STUArray s Int Int8
ar
forall {m :: * -> *}.
MArray (STUArray s) Int8 m =>
Int -> Int -> m ()
note Int
2 Int
0
forall {m :: * -> *}.
MArray (STUArray s) Int8 m =>
Int -> Int -> m ()
note Int
6 Int
3
forall {m :: * -> *}.
MArray (STUArray s) Int8 m =>
Int -> Int -> m ()
note Int
10 Int
5
forall {m :: * -> *}.
MArray (STUArray s) Int8 m =>
Int -> Int -> m ()
note Int
14 Int
7
forall {m :: * -> *}.
MArray (STUArray s) Int8 m =>
Int -> Int -> m ()
note Int
22 Int
11
forall {m :: * -> *}.
MArray (STUArray s) Int8 m =>
Int -> Int -> m ()
note Int
26 Int
13
forall {m :: * -> *}.
MArray (STUArray s) Int8 m =>
Int8 -> Int -> m (STUArray s Int Int8)
accumulate Int8
2 Int
3
cpGpAr :: UArray Int Int8
cpGpAr :: UArray Int Int8
cpGpAr = forall i e. (forall s. ST s (STUArray s i e)) -> UArray i e
runSTUArray forall a b. (a -> b) -> a -> b
$ do
STUArray s Int Int8
ar <- forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
(i, i) -> e -> m (a i e)
newArray (Int
0,Int
30030) Int8
0
forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> e -> m ()
unsafeWrite STUArray s Int Int8
ar Int
30030 Int8
1
let note :: Int -> Int -> m ()
note Int
s Int
i
| Int
i forall a. Ord a => a -> a -> Bool
< Int
30029 = forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> e -> m ()
unsafeWrite STUArray s Int Int8
ar Int
i Int8
1 forall (m :: * -> *) a b. Monad m => m a -> m b -> m b
>> Int -> Int -> m ()
note Int
s (Int
iforall a. Num a => a -> a -> a
+Int
s)
| Bool
otherwise = forall (m :: * -> *) a. Monad m => a -> m a
return ()
accumulate :: Int8 -> Int -> m (STUArray s Int Int8)
accumulate Int8
d Int
i
| Int
i forall a. Ord a => a -> a -> Bool
< Int
1 = forall (m :: * -> *) a. Monad m => a -> m a
return STUArray s Int Int8
ar
| Bool
otherwise = do
Int8
v <- forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> m e
unsafeRead STUArray s Int Int8
ar Int
i
if Int8
v forall a. Eq a => a -> a -> Bool
== Int8
0
then Int8 -> Int -> m (STUArray s Int Int8)
accumulate Int8
2 (Int
iforall a. Num a => a -> a -> a
-Int
2)
else do forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> e -> m ()
unsafeWrite STUArray s Int Int8
ar Int
i Int8
d
Int8 -> Int -> m (STUArray s Int Int8)
accumulate (Int8
dforall a. Num a => a -> a -> a
+Int8
1) (Int
iforall a. Num a => a -> a -> a
-Int
1)
forall {m :: * -> *}.
MArray (STUArray s) Int8 m =>
Int -> Int -> m ()
note Int
2 Int
0
forall {m :: * -> *}.
MArray (STUArray s) Int8 m =>
Int -> Int -> m ()
note Int
6 Int
3
forall {m :: * -> *}.
MArray (STUArray s) Int8 m =>
Int -> Int -> m ()
note Int
10 Int
5
forall {m :: * -> *}.
MArray (STUArray s) Int8 m =>
Int -> Int -> m ()
note Int
14 Int
7
forall {m :: * -> *}.
MArray (STUArray s) Int8 m =>
Int -> Int -> m ()
note Int
22 Int
11
forall {m :: * -> *}.
MArray (STUArray s) Int8 m =>
Int -> Int -> m ()
note Int
26 Int
13
forall {m :: * -> *}.
MArray (STUArray s) Int8 m =>
Int8 -> Int -> m (STUArray s Int Int8)
accumulate Int8
2 Int
30027
rMASK :: Int
rMASK :: Int
rMASK = forall b. FiniteBits b => b -> Int
finiteBitSize (Word
0 :: Word) forall a. Num a => a -> a -> a
- Int
1
wSHFT :: (Bits a, Num a) => a
wSHFT :: forall a. (Bits a, Num a) => a
wSHFT = if forall b. FiniteBits b => b -> Int
finiteBitSize (Word
0 :: Word) forall a. Eq a => a -> a -> Bool
== Int
64 then a
6 else a
5
tOPB :: Int
tOPB :: Int
tOPB = forall b. FiniteBits b => b -> Int
finiteBitSize (Word
0 :: Word) forall a. Bits a => a -> Int -> a
`shiftR` Int
1
tOPM :: (Bits a, Num a) => a
tOPM :: forall a. (Bits a, Num a) => a
tOPM = (a
1 forall a. Bits a => a -> Int -> a
`shiftL` Int
tOPB) forall a. Num a => a -> a -> a
- a
1
countToNth :: Int -> [PrimeSieve] -> Integer
countToNth :: Int -> [PrimeSieve] -> Integer
countToNth !Int
_ [] = forall a. HasCallStack => [Char] -> a
error [Char]
"countToNth: Prime stream ended prematurely"
countToNth !Int
n (PS Integer
v0 UArray Int Bool
bs : [PrimeSieve]
more) = Int -> Int -> Integer
go Int
n Int
0
where
wa :: UArray Int Word
wa :: UArray Int Word
wa = forall a b. a -> b
unsafeCoerce UArray Int Bool
bs
go :: Int -> Int -> Integer
go !Int
k Int
i
| Int
i forall a. Eq a => a -> a -> Bool
== forall a b. (a, b) -> b
snd (forall (a :: * -> * -> *) e i.
(IArray a e, Ix i) =>
a i e -> (i, i)
bounds UArray Int Word
wa)
= Int -> [PrimeSieve] -> Integer
countToNth Int
k [PrimeSieve]
more
| Bool
otherwise
= let w :: Word
w = forall (a :: * -> * -> *) e i.
(IArray a e, Ix i) =>
a i e -> Int -> e
unsafeAt UArray Int Word
wa Int
i
bc :: Int
bc = forall a. Bits a => a -> Int
popCount Word
w
in if Int
bc forall a. Ord a => a -> a -> Bool
< Int
k
then Int -> Int -> Integer
go (Int
kforall a. Num a => a -> a -> a
-Int
bc) (Int
iforall a. Num a => a -> a -> a
+Int
1)
else let j :: Int
j = Int
bc forall a. Num a => a -> a -> a
- Int
k
px :: Int
px = Word -> Int -> Int -> Int
top Word
w Int
j Int
bc
in Integer
v0 forall a. Num a => a -> a -> a
+ forall a. Num a => Int -> a
toPrim (Int
px forall a. Num a => a -> a -> a
+ (Int
i forall a. Bits a => a -> Int -> a
`shiftL` forall a. (Bits a, Num a) => a
wSHFT))
countAll :: PrimeSieve -> Int
countAll :: PrimeSieve -> Int
countAll (PS Integer
_ UArray Int Bool
bs) = Int -> Int -> Int
go Int
0 Int
0
where
wa :: UArray Int Word
wa :: UArray Int Word
wa = forall a b. a -> b
unsafeCoerce UArray Int Bool
bs
go :: Int -> Int -> Int
go !Int
ct Int
i
| Int
i forall a. Eq a => a -> a -> Bool
== forall a b. (a, b) -> b
snd (forall (a :: * -> * -> *) e i.
(IArray a e, Ix i) =>
a i e -> (i, i)
bounds UArray Int Word
wa)
= Int
ct
| Bool
otherwise
= Int -> Int -> Int
go (Int
ct forall a. Num a => a -> a -> a
+ forall a. Bits a => a -> Int
popCount (forall (a :: * -> * -> *) e i.
(IArray a e, Ix i) =>
a i e -> Int -> e
unsafeAt UArray Int Word
wa Int
i)) (Int
iforall a. Num a => a -> a -> a
+Int
1)
top :: Word -> Int -> Int -> Int
top :: Word -> Int -> Int -> Int
top Word
w Int
j Int
bc = forall {t}. (Num t, Bits t) => Int -> Int -> t -> Int -> t -> Int
go Int
0 Int
tOPB forall a. (Bits a, Num a) => a
tOPM Int
bn Word
w
where
!bn :: Int
bn = Int
bcforall a. Num a => a -> a -> a
-Int
j
go :: Int -> Int -> t -> Int -> t -> Int
go !Int
_ Int
_ !t
_ !Int
_ t
0 = forall a. HasCallStack => [Char] -> a
error [Char]
"Too few bits set"
go Int
bs Int
0 t
_ Int
_ t
wd = if t
wd forall a. Bits a => a -> a -> a
.&. t
1 forall a. Eq a => a -> a -> Bool
== t
0 then forall a. HasCallStack => [Char] -> a
error [Char]
"Too few bits, shift 0" else Int
bs
go Int
bs Int
a t
msk Int
ix t
wd =
case forall a. Bits a => a -> Int
popCount (t
wd forall a. Bits a => a -> a -> a
.&. t
msk) of
Int
lc | Int
lc forall a. Ord a => a -> a -> Bool
< Int
ix -> Int -> Int -> t -> Int -> t -> Int
go (Int
bsforall a. Num a => a -> a -> a
+Int
a) Int
a t
msk (Int
ixforall a. Num a => a -> a -> a
-Int
lc) (t
wd forall a. Bits a => a -> Int -> a
`unsafeShiftR` Int
a)
| Bool
otherwise ->
let !na :: Int
na = Int
a forall a. Bits a => a -> Int -> a
`shiftR` Int
1
in Int -> Int -> t -> Int -> t -> Int
go Int
bs Int
na (t
msk forall a. Bits a => a -> Int -> a
`unsafeShiftR` Int
na) Int
ix t
wd
countFromTo :: Int -> Int -> STUArray s Int Bool -> ST s Int
countFromTo :: forall s. Int -> Int -> STUArray s Int Bool -> ST s Int
countFromTo Int
start Int
end STUArray s Int Bool
ba = do
STUArray s Int Word
wa <- (forall s ix a b. STUArray s ix a -> ST s (STUArray s ix b)
castSTUArray :: STUArray s Int Bool -> ST s (STUArray s Int Word)) STUArray s Int Bool
ba
let !sb :: Int
sb = Int
start forall a. Bits a => a -> Int -> a
`shiftR` forall a. (Bits a, Num a) => a
wSHFT
!si :: Int
si = Int
start forall a. Bits a => a -> a -> a
.&. Int
rMASK
!eb :: Int
eb = Int
end forall a. Bits a => a -> Int -> a
`shiftR` forall a. (Bits a, Num a) => a
wSHFT
!ei :: Int
ei = Int
end forall a. Bits a => a -> a -> a
.&. Int
rMASK
count :: Int -> Int -> m Int
count !Int
acc Int
i
| Int
i forall a. Eq a => a -> a -> Bool
== Int
eb = do
Word
w <- forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> m e
unsafeRead STUArray s Int Word
wa Int
i
forall (m :: * -> *) a. Monad m => a -> m a
return (Int
acc forall a. Num a => a -> a -> a
+ forall a. Bits a => a -> Int
popCount (Word
w forall a. Bits a => a -> Int -> a
`shiftL` (Int
rMASK forall a. Num a => a -> a -> a
- Int
ei)))
| Bool
otherwise = do
Word
w <- forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> m e
unsafeRead STUArray s Int Word
wa Int
i
Int -> Int -> m Int
count (Int
acc forall a. Num a => a -> a -> a
+ forall a. Bits a => a -> Int
popCount Word
w) (Int
iforall a. Num a => a -> a -> a
+Int
1)
if Int
sb forall a. Ord a => a -> a -> Bool
< Int
eb
then do
Word
w <- forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> m e
unsafeRead STUArray s Int Word
wa Int
sb
forall {m :: * -> *}.
MArray (STUArray s) Word m =>
Int -> Int -> m Int
count (forall a. Bits a => a -> Int
popCount (Word
w forall a. Bits a => a -> Int -> a
`shiftR` Int
si)) (Int
sbforall a. Num a => a -> a -> a
+Int
1)
else do
Word
w <- forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> Int -> m e
unsafeRead STUArray s Int Word
wa Int
sb
let !w1 :: Word
w1 = Word
w forall a. Bits a => a -> Int -> a
`shiftR` Int
si
forall (m :: * -> *) a. Monad m => a -> m a
return (forall a. Bits a => a -> Int
popCount (Word
w1 forall a. Bits a => a -> Int -> a
`shiftL` (Int
rMASK forall a. Num a => a -> a -> a
- Int
ei forall a. Num a => a -> a -> a
+ Int
si)))