CLI interface + restructuration + precision fixes Fermat Factorization

README.md

@@ -2,8 +2,9 @@
 
 ## running project from CLI
 ```
-$ ghci -i./src
+$ cabal update
-ghci> :load HaskellMath.hs
+$ cabal build
+$ cabal run
 ```
 
 ## algorithms

app/FactorizationUI.hs

@@ -0,0 +1,36 @@
+module FactorizationUI (run) where
+
+import Utils (askChoice, askNumber)
+import Factorization (fermatFactorization, pollardPminus1)
+
+run :: IO ()
+run = do
+    putStrLn "Factorization"
+    putStrLn "1) Fermat factorization"
+    putStrLn "2) Pollard p-1"
+
+    choice <- askChoice 2
+
+    case choice of
+        1 -> fermatUI
+        2 -> pollardUI
+        _ -> error "Impossible"
+
+fermatUI :: IO ()
+fermatUI = do
+    n <- askNumber "Enter an integer n > 1:"
+    let (p, q) = fermatFactorization n
+    putStrLn ("n = " ++ show n)
+    putStrLn ("p = " ++ show p)
+    putStrLn ("q = " ++ show q)
+
+pollardUI :: IO ()
+pollardUI = do
+    n <- askNumber "Enter an integer n > 1:"
+    b <- askNumber "Enter the bound B:"
+    case pollardPminus1 n b of
+        Just factor -> do
+            putStrLn ("Found factor: " ++ show factor)
+            putStrLn ("Other factor: " ++ show (n `div` factor))
+        Nothing ->
+            putStrLn "Failed to find a factor (try a different B or method)."

app/Main.hs

@@ -1,7 +1,19 @@
 module Main where
 
-import qualified Primes ()
+import Utils (askChoice)
+import qualified FactorizationUI
 
 main :: IO ()
 main = do
-  putStrLn "unimplemented"
+    putStrLn "Haskell Math Toolkit"
+    putStrLn "1) Factorization"
+    putStrLn "2) Modular square root (not yet implemented)"
+    putStrLn "3) Primality test (not yet implemented)"
+
+    choice <- askChoice 3
+
+    case choice of
+        1 -> FactorizationUI.run
+        2 -> putStrLn "Modular square root: not implemented yet."
+        3 -> putStrLn "Primality test: not implemented yet."
+        _ -> error "Impossible"

app/Utils.hs

@@ -1,4 +1,4 @@
-module Utils (askNumber) where
+module Utils (askNumber, askChoice) where
 
 import Text.Read (readMaybe)
 import System.Exit (exitSuccess)
@@ -13,3 +13,13 @@ askNumber s = do
         _ -> do
             putStrLn "Not a valid integer"
             exitSuccess
+
+askChoice :: Int -> IO Int
+askChoice maxChoice = do
+    putStrLn "Enter your choice:"
+    input <- getLine
+    case readMaybe input of
+        Just n | n >= 1 && n <= maxChoice -> return n
+        _ -> do
+            putStrLn "Invalid choice"
+            exitSuccess

haskell-math.cabal

@@ -20,10 +20,16 @@ library
     import:           warnings
     exposed-modules:
         Primes
+        Factorization
+        ModularSquareRoot
+        ModularArithmeticUtils
     other-modules:
+        Primes.FermatPrimeTest
         Primes.MillerRabin
         Primes.SolovayStrassen
-        ModularArithmeticUtils
+        Factorization.FermatFactorization
+        Factorization.PollardPminus1
+        ModularSquareRoot.TonelliShanks
     build-depends:
         base ^>=4.18.2.1,
         random ^>=1.2
@@ -33,6 +39,9 @@ library
 executable haskell-math
     import:           warnings
     main-is:          Main.hs
+    other-modules:
+        FactorizationUI
+        Utils
     build-depends:
         base ^>=4.18.2.1,
         haskell-math

src/Factorization.hs

@@ -0,0 +1,4 @@
+module Factorization ( fermatFactorization, pollardPminus1) where
+
+import Factorization.FermatFactorization
+import Factorization.PollardPminus1

src/Factorization/FermatFactorization.hs

@@ -0,0 +1,31 @@
+module Factorization.FermatFactorization (fermatFactorization) where
+
+fermatFactorization :: Integer -> (Integer, Integer)
+fermatFactorization n
+  | n <= 0        = error "n must be positive"
+  | even n        = (2, n `div` 2)
+  | otherwise     = (p, q)
+  where
+    (d, root) = findIntegerSqrt n
+    p = root + d
+    q = root - d
+
+-- Find the smallest integer d >= 0 such that sqrt(n + d^2) is an integer
+findIntegerSqrt :: Integer -> (Integer, Integer)
+findIntegerSqrt n = go 0
+  where
+    go d =
+      let val  = n + d*d
+          root = isqrt val
+      in if root * root == val
+         then (d, root)
+         else go (d + 1)
+
+isqrt :: Integer -> Integer
+isqrt 0 = 0
+isqrt 1 = 1
+isqrt n = iterateSqrt n
+  where
+    iterateSqrt x =
+      let y = (x + n `div` x) `div` 2
+      in if y >= x then x else iterateSqrt y

src/Factorization/PollardPminus1.hs

@@ -1,25 +1,10 @@
-import Text.Read (readMaybe)
+module Factorization.PollardPminus1 (pollardPminus1) where
-import System.Exit (exitSuccess)
+
-import Utils (askNumber)
 import ModularArithmeticUtils (modExp)
 
-main :: IO ()
-main = do
-    n <- askNumber "Enter an integer n>1 to factor:"
-    b <- askNumber "Enter the bound B:"
-    putStrLn ("n = " ++ show n)
-
-    case pollardP1 n b of
-        Just factor -> do
-            putStrLn ("Found factor: " ++ show factor)
-            let otherFactor = n `div` factor
-            putStrLn ("Other factor: " ++ show otherFactor)
-        Nothing -> do
-            putStrLn "Failed to find a factor using Pollard p-1 method. n could be prime or different parameters needed."
-
 -- Pollard p-1 factorization algorithm
-pollardP1 :: Integer -> Integer -> Maybe Integer
+pollardPminus1 :: Integer -> Integer -> Maybe Integer
-pollardP1 n b = tryBases [2..5]
+pollardPminus1 n b = tryBases [2..5]
   where
     tryBases [] = Nothing
     tryBases (a:as) =

src/Factorization/fermat-factorization.hs

@@ -1,24 +0,0 @@
-import Text.Read (readMaybe)
-import System.Exit (exitSuccess)
-import Utils (askNumber)
-
-main :: IO ()
-main = do
-    n <- askNumber "Enter an integer:"
-    let (d, root) = findIntegerSqrt n
-        q = (root - d)
-        p = (root + d)
-    putStrLn ("n = " ++ show n)
-    putStrLn ("Found d = " ++ show d ++ ", sqrt(n + d^2) = " ++ show root)
-    putStrLn ("q = " ++ show q ++ ", p = " ++ show p)
-
--- Find the smallest integer d >= 0 such that sqrt(n + d^2) is an integer
-findIntegerSqrt :: Integer -> (Integer, Integer)
-findIntegerSqrt n = go 0
-  where
-    go d =
-        let val  = n + d*d
-            root = floor (sqrt (fromIntegral val))
-        in if root * root == val
-           then (d, root)
-           else go (d + 1)

src/ModularSquareRoot.hs

@@ -0,0 +1,3 @@
+module ModularSquareRoot (tonelliShanks) where
+
+import ModularSquareRoot.TonelliShanks

src/ModularSquareRoot/TonelliShanks.hs

@@ -1,4 +1,4 @@
-module TonelliShanks (tonelliShanks) where
+module ModularSquareRoot.TonelliShanks (tonelliShanks) where
 
 import ModularArithmeticUtils (modExp, modMul, legendre, factorOutTwos)