Initial commit!

.gitignore

@@ -0,0 +1,7 @@
+/target
+**/*.rs.bk
+Cargo.lock
+
+generate.hi
+generate.o
+generate

Cargo.toml

@@ -0,0 +1,6 @@
+[package]
+name = "cryptonum"
+version = "0.1.0"
+authors = ["awick"]
+
+[dependencies]

generate.hs

@@ -0,0 +1,243 @@
+import Control.Monad(foldM_,forM_,when)
+import Data.Bits(shiftL,shiftR)
+import Data.List(sort)
+import qualified Data.Map.Strict as Map
+import Numeric(showHex)
+import Prelude hiding (log)
+import System.Directory(createDirectoryIfMissing)
+import System.Environment(getArgs)
+import System.FilePath((</>))
+import System.IO(Handle,IOMode(WriteMode),hPutStrLn,withFile,hFlush,hPutStr,stderr)
+import System.Random(StdGen,newStdGen,random,split)
+
+data Level = Base | DivMul | Barrett
+ deriving (Eq, Ord, Show)
+
+bitSizes :: [Int]
+bitSizes =  [192,256,384,512,576,1024,2048,3072,4096,7680,8192,15360]
+
+numberOfTests :: Int
+numberOfTests = 1000
+
+baseMap :: Map.Map Int Level
+baseMap = foldr (\ s m -> Map.insert s Barrett m) Map.empty bitSizes
+
+smartInsert :: Int -> Level -> Map.Map Int Level -> Map.Map Int Level
+smartInsert size level map = Map.insertWith max size level map
+
+generateNext :: Int -> Level -> Map.Map Int Level -> Map.Map Int Level
+generateNext size Base    acc = acc
+generateNext size DivMul  acc = smartInsert (size + 64) Base $
+                                smartInsert (size * 2)  Base $
+                                acc
+generateNext size Barrett acc = smartInsert (size + 64)       Base   $
+                                smartInsert (size * 2)        Base   $
+                                smartInsert ( size      + 64) DivMul $
+                                smartInsert ((size * 2) + 64) DivMul $
+                                acc
+
+step :: Map.Map Int Level -> Map.Map Int Level
+step m = Map.foldrWithKey generateNext m m
+
+fixpoint :: Map.Map Int Level -> Map.Map Int Level
+fixpoint m | m == m'   = m
+           | otherwise = fixpoint m'
+ where m' = step m
+
+finalMap :: Map.Map Int Level
+finalMap = fixpoint baseMap
+
+conversions :: [Int] -> [(Int,Int)]
+conversions []       = []
+conversions (x:rest) = (map (\ y -> (x,y)) rest) ++ conversions rest
+
+generateTestBlock :: Handle -> String -> IO ()
+generateTestBlock hndl name =
+  do hPutStrLn hndl ("  mod " ++ name ++ " {")
+     hPutStrLn hndl ("    use super::super::*;\n")
+     hPutStrLn hndl ("    use testing::run_test;\n")
+     forM_ (sort (Map.toList finalMap)) $ \ (size, kind) ->
+       when (kind >= Base) $
+         hPutStrLn hndl ("    generate_" ++ name ++ 
+                         "_tests!(U" ++ show size ++ ");")
+     hPutStrLn hndl "  }"
+
+generateInvocs :: IO ()
+generateInvocs =
+  withFile "src/unsigned/invoc.rs" WriteMode $ \ hndl ->
+    do forM_ (sort (Map.toList finalMap)) $ \ item ->
+         case item of
+           (size, Base) ->
+             hPutStrLn hndl ("generate_number!(U" ++ show size ++ ", " ++
+                             show (size `div` 64) ++ ");")
+           (size, DivMul) ->
+             hPutStrLn hndl ("generate_number!(U" ++ show size ++ ", " ++
+                             show (size `div` 64) ++ ", U" ++
+                             show (size + 64) ++ ", U" ++
+                             show (size * 2) ++ ");")
+           (size, Barrett) ->
+             hPutStrLn hndl ("generate_number!(U" ++ show size ++ ", " ++
+                             show (size `div` 64) ++ ", U" ++
+                             show (size + 64) ++ ", U" ++
+                             show (size * 2) ++ ", U" ++
+                             show ((size * 2) + 64) ++ ", BarrettU" ++
+                             show size ++ ");")
+       hPutStrLn hndl ""
+       forM_ (conversions (Map.keys finalMap)) $ \ (a,b) ->
+         hPutStrLn hndl ("conversion_impls!(U" ++ show a ++ ", " ++
+                         "U" ++ show b ++ ");")
+       hPutStrLn hndl "\n#[cfg(test)]"
+       hPutStrLn hndl "mod tests {"
+       generateTestBlock hndl "base"
+       hPutStrLn hndl "}"
+
+log :: String -> IO ()
+log str = hPutStr stderr str >> hFlush stderr
+
+generateTests :: Level -> String -> a -> (Int -> a -> (Map.Map String String, a)) -> IO ()
+generateTests minLevel directory init runner =
+  forM_  (sort (Map.toList finalMap)) $ \ (size, myLevel) ->
+    when (myLevel >= minLevel) $
+      do createDirectoryIfMissing True ("testdata" </> directory)
+         log $ "Generating " ++ show size ++ "-bit " ++ directory ++ " tests "
+         let dest = "testdata" </> directory </> ("U" ++ show size ++ ".tests") 
+         withFile dest WriteMode $ \ hndl ->
+           foldM_ (writer hndl size runner) init [0..numberOfTests]
+         log "done.\n"
+ where
+  writer :: Handle -> Int -> (Int -> a -> (Map.Map String String, a)) -> a -> Int -> IO a
+  writer hndl size runner input _ =
+    do let (output, acc) = runner size input
+       forM_ (Map.toList output) $ \ (key, val) ->
+         do hPutStrLn hndl (key ++ ": " ++ val)
+            log "."
+       return acc
+
+type Database = (Map.Map String [Integer], StdGen)
+
+emptyDatabase :: StdGen -> (Database, StdGen)
+emptyDatabase g0 =
+  let (g, g') = split g0
+  in ((Map.empty, g), g')
+
+generateNum :: Database -> String -> Int -> (Integer, Database)
+generateNum (db, rng0) varname size =
+  let (x, rng1) = random rng0
+      x'        = modulate x size
+      before    = Map.findWithDefault [] varname db
+  in if length (filter (== x') before) < 10
+       then (x', (Map.insert varname (x':before) db, rng1))
+       else generateNum (db, rng1) varname size
+
+modulate :: Integer -> Int -> Integer
+modulate x size = x `mod` (2 ^ size)
+
+showX :: (Integral a, Show a) => a -> String
+showX x = showHex x ""
+
+showB :: Bool -> String
+showB False = "0"
+showB True  = "1"
+
+base :: Integer
+base = 2 ^ (64 :: Integer)
+
+barrett :: Integer -> Integer
+barrett m = (base ^ (2 * k)) `div` m
+ where
+  k = computeK m
+
+computeK :: Integer -> Int
+computeK v = go 0 1
+ where
+  go k acc | v <= acc  = k
+           | otherwise = go (k + 1) (acc * base)
+
+generateAllTheTests :: IO ()
+generateAllTheTests =
+  do gen0 <- newStdGen
+     let (db1, gen1) = emptyDatabase gen0
+     generateTests DivMul "add" db1 $ \ size memory0 ->
+       let (a, memory1) = generateNum memory0 "a" size
+           (b, memory2) = generateNum memory1 "b" size
+           c            = modulate    (a + b)     size
+       in (Map.fromList [("a", showX a), ("b", showX b), ("c", showX c)], memory2)
+     let (db2, gen2) = emptyDatabase gen1
+     generateTests Barrett "barrett_gen" db2 $ \ size memory0 ->
+       let (m, memory1) = generateNum memory0 "m" size
+           k            = computeK m
+           u            = barrett m
+       in (Map.fromList [("m", showX m), ("k", showX k), ("u", showX u)], memory1)
+     let (db3, gen3) = emptyDatabase gen1
+     generateTests Barrett "barrett_reduce" db3 $ \ size memory0 ->
+       let (m, memory1) = generateNum memory0 "m" size
+           (x, memory2) = generateNum memory1 "x" (min size (2 * k * 64))
+           k            = computeK m
+           u            = barrett m
+           r            = x `mod` m
+           res          = Map.fromList [("m", showX m), ("x", showX x),
+                                        ("k", showX k), ("u", showX u),
+                                        ("r", showX r)]
+       in (res, memory2)
+     let (db4, gen4) = emptyDatabase gen2
+     generateTests Base "base" db4 $ \ size memory0 ->
+       let (x, memory1) = generateNum memory0 "x" size
+           (m, memory2) = generateNum memory1 "m" size
+           m'           = m `mod` (fromIntegral size `div` 64)
+           r            = x `mod` (2 ^ (64 * m'))
+           res          = Map.fromList [("x", showX x),        ("z", showB (x == 0)),
+                                        ("e", showB (even x)), ("o", showB (odd x)),
+                                        ("m", showX m'),       ("r", showX r)]
+       in (res, memory2)
+     let (db5, gen5) = emptyDatabase gen3
+     generateTests Base "cmp" db5 $ \ size memory0 ->
+       let (a, memory1) = generateNum memory0 "a" size
+           (b, memory2) = generateNum memory1 "b" size
+           res          = Map.fromList [("a", showX a), ("b", showX b),
+                                        ("g", showB (a > b)), ("l", showB (a < b)),
+                                        ("e", showB (a == b))]
+       in (res, memory2)
+     let (db6, gen6) = emptyDatabase gen4
+     generateTests DivMul "div" db6 $ \ size memory0 ->
+       let (a, memory1) = generateNum memory0 "a" size
+           (b, memory2) = generateNum memory1 "b" size
+           res          = Map.fromList [("a", showX a), ("b", showX b), ("c", showX (a `div` b))]
+       in (res, memory2)
+     let (db7, gen7) = emptyDatabase gen5
+     generateTests DivMul "mul" db7 $ \ size memory0 ->
+       let (a, memory1) = generateNum memory0 "a" size
+           (b, memory2) = generateNum memory1 "b" size
+           c            = a * b
+           d            = modulate c size
+           res          = Map.fromList [("a", showX a), ("b", showX b),
+                                        ("c", showX c), ("d", showX d)]
+       in (res, memory2)
+     let (db8, gen8) = emptyDatabase gen6
+     generateTests Base "shiftl" db8 $ \ size memory0 ->
+       let (a, memory1) = generateNum memory0 "a" size
+           (l, memory2) = generateNum memory1 "l" size
+           l'           = l `mod` fromIntegral (computeK a * 64)
+           r            = modulate (a `shiftL` fromIntegral l') size
+           res          = Map.fromList [("a", showX a), ("l", showX l'), ("r", showX r)]
+       in (res, memory2)
+     let (db9, gen9) = emptyDatabase gen6
+     generateTests Base "shiftr" db9 $ \ size memory0 ->
+       let (a, memory1) = generateNum memory0 "a" size
+           (l, memory2) = generateNum memory1 "l" size
+           l'           = l `mod` fromIntegral (computeK a * 64)
+           r            = modulate (a `shiftR` fromIntegral l') size
+           res          = Map.fromList [("a", showX a), ("l", showX l'), ("r", showX r)]
+       in (res, memory2)
+     let (dbA, genA) = emptyDatabase gen7
+     generateTests Base "sub" dbA $ \ size memory0 ->
+       let (a, memory1) = generateNum memory0 "a" size
+           (b, memory2) = generateNum memory1 "b" size
+           c            = modulate    (a - b)     size
+       in (Map.fromList [("a", showX a), ("b", showX b), ("c", showX c)], memory2)
+
+main :: IO ()
+main =
+  do args <- getArgs
+     let args' = if null args then ["invocs", "test"] else args
+     when ("invocs" `elem` args') generateInvocs
+     when ("tests"  `elem` args') generateAllTheTests

src/lib.rs

@@ -0,0 +1,4 @@
+#![recursion_limit="1024"]
+pub mod unsigned;
+#[cfg(test)]
+pub mod testing;

src/testing.rs

@@ -0,0 +1,62 @@
+use std::collections::HashMap;
+use std::fs::File;
+use std::io::Read;
+use std::str::Lines;
+
+fn next_value_set(line: &str) -> (String, bool, Vec<u8>)
+{
+    assert!(line.is_ascii());
+    let mut items = line.split(": ");
+    let key = items.next().unwrap();
+    let valbits = items.next().unwrap();
+    let neg = valbits.contains('-');
+    let valbitsnoneg = valbits.trim_left_matches("-");
+
+    let mut nibble_iter = valbitsnoneg.chars().rev();
+    let mut val = Vec::new();
+
+    while let Some(c1) = nibble_iter.next() {
+        match nibble_iter.next() {
+            None => {
+                val.push( c1.to_digit(16).unwrap() as u8 );
+            }
+            Some(c2) => {
+                let b1 = c1.to_digit(16).unwrap() as u8;
+                let b2 = c2.to_digit(16).unwrap() as u8;
+                val.push( (b2 << 4) | b1 );
+            }
+        }
+    }
+    val.reverse();
+
+    (key.to_string(), neg, val)
+}
+
+fn next_test_case(contents: &mut Lines, lines: usize) ->
+    Option<HashMap<String,(bool,Vec<u8>)>>
+{
+    let mut res = HashMap::new();
+    let mut count = 0;
+
+    while count < lines {
+        let line = contents.next()?;
+        let (key, neg, val) = next_value_set(line);
+        res.insert(key, (neg,val));
+        count += 1;
+    }
+
+    Some(res)
+}
+
+pub fn run_test<F>(fname: String, i: usize, f: F)
+ where F: Fn(HashMap<String,(bool,Vec<u8>)>)
+{
+    let mut file = File::open(fname).unwrap();
+    let mut contents = String::new();
+    file.read_to_string(&mut contents).unwrap();
+    let mut iter = contents.lines();
+
+    while let Some(scase) = next_test_case(&mut iter, i) {
+        f(scase);
+    }
+}

src/unsigned/add.rs

@@ -0,0 +1,98 @@
+pub fn addition(dest: &mut [u64], src: &[u64])
+{
+    assert_eq!(dest.len(), src.len() + 1);
+    let mut carry: u128 = 0;
+
+    for i in 0..src.len() {
+        let x128 = dest[i] as u128;
+        let y128 = src[i] as u128;
+        let z128 = x128 + y128 + carry;
+
+        dest[i] = z128 as u64;
+        carry = z128 >> 64;
+    }
+    dest[src.len()] = carry as u64;
+}
+
+pub fn unsafe_addition(dest: &mut [u64], src: &[u64])
+{
+    assert_eq!(dest.len(), src.len());
+    let mut carry: u128 = 0;
+
+    for i in 0..src.len() {
+        let x128 = dest[i] as u128;
+        let y128 = src[i] as u128;
+        let z128 = x128 + y128 + carry;
+
+        dest[i] = z128 as u64;
+        carry = z128 >> 64;
+    }
+    assert_eq!(carry, 0, "Unsafe overflow in AddAssign");
+}
+
+macro_rules! addition_impls
+{
+    ($base: ident, $bigger: ident) => {
+        impl AddAssign<$base> for $base {
+            fn add_assign(&mut self, rhs: $base) {
+                unsafe_addition(&mut self.value, &rhs.value);
+            }
+        }
+
+        impl<'a> AddAssign<&'a $base> for $base {
+            fn add_assign(&mut self, rhs: &$base) {
+                unsafe_addition(&mut self.value, &rhs.value);
+            }
+        }
+
+        impl Add<$base> for $base {
+            type Output = $bigger;
+
+            fn add(self, rhs: $base) -> $bigger
+            {
+                let mut dest = $bigger::zero();
+                &dest.value[0..rhs.value.len()].copy_from_slice(&self.value);
+                addition(&mut dest.value, &rhs.value);
+                dest
+            }
+        }
+
+        impl<'a> Add<&'a $base> for $base {
+            type Output = $bigger;
+
+            fn add(self, rhs: &$base) -> $bigger
+            {
+                let mut dest = $bigger::zero();
+                &dest.value[0..rhs.value.len()].copy_from_slice(&self.value);
+                addition(&mut dest.value, &rhs.value);
+                dest
+            }
+        }
+
+        impl<'a> Add<$base> for &'a $base {
+            type Output = $bigger;
+
+            fn add(self, rhs: $base) -> $bigger
+            {
+                let mut dest = $bigger::zero();
+                &dest.value[0..rhs.value.len()].copy_from_slice(&self.value);
+                addition(&mut dest.value, &rhs.value);
+                dest
+            }
+        }
+
+        impl<'a,'b> Add<&'a $base> for &'b $base {
+            type Output = $bigger;
+
+            fn add(self, rhs: &$base) -> $bigger
+            {
+                let mut dest = $bigger::zero();
+                &dest.value[0..rhs.value.len()].copy_from_slice(&self.value);
+                addition(&mut dest.value, &rhs.value);
+                dest
+            }
+        }
+    }
+}
+
+//addition_impls!(U192,   U256);

src/unsigned/barrett.rs

@@ -0,0 +1,59 @@
+macro_rules! barrett_impl {
+    ($bar: ident, $name: ident, $name64: ident, $dbl: ident, $dbl64: ident) => {
+       pub struct $bar {
+           pub(crate) k:  usize,
+           pub(crate) m:  $name64,
+           pub(crate) mu: $name64
+       }
+
+       impl $bar {
+           pub fn new(m: $name) -> $bar {
+                // Step #1: Figure out k
+                let mut k = 0;
+                for i in 0..m.value.len() {
+                    if m.value[i] != 0 {
+                        k = i;
+                    }
+                }
+                k += 1;
+                // Step #2: Compute b
+                let mut b = $dbl64::zero();
+                b.value[2*k] = 1;
+                // Step #3: Divide b by m.
+                let bigm = $dbl64::from(&m);
+                let quot = b / &bigm;
+                let resm = $name64::from(&m);
+                let mu = $name64::from(&quot);
+                // Done!
+                $bar { k: k, m: resm, mu: mu }
+           }
+           
+           pub fn reduce(&self, x: &$dbl) -> $name {
+                let     m2: $dbl64  = $dbl64::from(&self.m);
+                // 1. q1←⌊x/bk−1⌋, q2←q1 · μ, q3←⌊q2/bk+1⌋.
+                let     q1: $name64 = $name64::from(x >> (self.k - 1));
+                let     q2: $dbl64  = $dbl64::from(q1 * &self.mu);
+                let     q3: $name64 = $name64::from(q2 >> (self.k + 1));
+                // 2. r1←x mod bk+1, r2←q3 · m mod bk+1, r←r1 − r2.
+                let mut r:  $dbl64  = $dbl64::from(x);
+                r.mask(self.k + 1);
+                let mut r2: $dbl64  = $dbl64::from(q3 * &self.m);
+                r2.mask(self.k + 1);
+                let went_negative = &r < &r2;
+                r -= &r2;
+                // 3. If r<0 then r←r+bk+1.
+                if went_negative {
+                    let mut bk1 = $dbl64::zero();
+                    bk1.value[self.k+1] = 1;
+                    r += &bk1;
+                }
+                // 4. While r≥m do: r←r−m.
+                while &r > &m2 {
+                    r -= &m2;
+                }
+                // Done!
+                $name::from(&r)
+           }
+       }
+    };
+}

src/unsigned/base.rs

@@ -0,0 +1,83 @@
+pub trait CryptoNum {
+    fn zero() -> Self;
+    fn is_zero(&self) -> bool;
+    fn is_even(&self) -> bool;
+    fn is_odd(&self) -> bool;
+    fn mask(&mut self, len: usize);
+}
+
+macro_rules! generate_base
+{
+    ($name: ident, $size: expr) => {
+        #[derive(Clone)]
+        pub struct $name {
+            pub(crate) value: [u64; $size]
+        }
+
+        impl CryptoNum for $name {
+            fn zero() -> $name {
+                $name{ value: [0; $size] }
+            }
+
+            fn is_zero(&self) -> bool {
+                self.value.iter().all(|&x| x == 0)
+            }
+
+            fn is_even(&self) -> bool {
+                (self.value[0] & 0x1) == 0
+            }
+
+            fn is_odd(&self) -> bool {
+                (self.value[0] & 0x1) == 1
+            }
+
+            fn mask(&mut self, len: usize) {
+                let dellen = min(len, $size);
+                for i in dellen..$size {
+                    self.value[i] = 0;
+                }
+            }
+        }
+    }
+}
+
+#[cfg(test)]
+macro_rules! generate_base_tests
+{
+    ($name: ident) => {
+        impl fmt::Debug for $name {
+            fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+                f.write_str(stringify!($name))?;
+                f.write_str("{")?;
+                f.debug_list().entries(self.value.iter()).finish()?;
+                f.write_str("}")
+            }
+        }
+
+        #[test]
+        #[allow(non_snake_case)]
+        fn $name() {
+            let fname = format!("testdata/base/{}.tests", stringify!($name));
+            run_test(fname.to_string(), 6, |case| {
+                let (neg0, xbytes) = case.get("x").unwrap();
+                let (neg1, mbytes) = case.get("m").unwrap();
+                let (neg2, zbytes) = case.get("z").unwrap();
+                let (neg3, ebytes) = case.get("e").unwrap();
+                let (neg4, obytes) = case.get("o").unwrap();
+                let (neg5, rbytes) = case.get("r").unwrap();
+                assert!(!neg0 && !neg1 && !neg2 && !neg3 && !neg4 && !neg5);
+                let mut x = $name::from_bytes(xbytes);
+                let m = $name::from_bytes(mbytes);
+                let z = 1 == zbytes[0];
+                let e = 1 == ebytes[0];
+                let o = 1 == obytes[0];
+                let r = $name::from_bytes(rbytes);
+                assert_eq!(x.is_zero(), z);
+                assert_eq!(x.is_even(), e);
+                assert_eq!(x.is_odd(),  o);
+                x.mask(usize::from(&m));
+                assert_eq!(x, r);
+            });
+        }
+    }
+}

src/unsigned/cmp.rs

@@ -0,0 +1,42 @@
+use std::cmp::*;
+
+pub fn compare(a: &[u64], b: &[u64]) -> Ordering {
+    assert_eq!(a.len(), b.len(), "Incompatible numbers in comparison");
+
+    let mut i = (a.len() - 1) as isize;
+
+    while i >= 0 {
+        let iu = i as usize;
+        match a[iu].cmp(&b[iu]) {
+            Ordering::Greater => return Ordering::Greater,
+            Ordering::Less    => return Ordering::Less,
+            Ordering::Equal   => i -= 1
+        }
+    }
+
+    Ordering::Equal
+}
+
+macro_rules! cmp_impls {
+    ($name: ident) => {
+        impl PartialEq for $name {
+            fn eq(&self, rhs: &$name) -> bool {
+                compare(&self.value, &rhs.value) == Ordering::Equal
+            }
+        }
+
+        impl Eq for $name {}
+
+        impl PartialOrd for $name {
+            fn partial_cmp(&self, rhs: &$name) -> Option<Ordering> {
+                Some(compare(&self.value, &rhs.value))
+            }
+        }
+
+        impl Ord for $name {
+            fn cmp(&self, rhs: &$name) -> Ordering {
+                compare(&self.value, &rhs.value)
+            }
+        }
+    }
+}

src/unsigned/codec.rs

@@ -0,0 +1,70 @@
+pub trait Decoder {
+    fn from_bytes(x: &[u8]) -> Self;
+}
+
+pub trait Encoder {
+    fn to_bytes(&self) -> Vec<u8>;
+}
+
+pub(crate) fn raw_decoder(input: &[u8], output: &mut [u64])
+{
+    let mut item = 0;
+    let mut shift = 0;
+    let mut idx = 0;
+
+    for v in input.iter().rev() {
+        item |= (*v as u64) << shift;
+        shift += 8;
+        if shift == 64 {
+            shift = 0;
+            output[idx] = item;
+            idx += 1;
+            item = 0;
+        }
+    }
+    if item != 0 {
+        output[idx] = item;
+    }
+}
+
+macro_rules! generate_decoder {
+    ($name: ident) => {
+        impl Decoder for $name {
+            fn from_bytes(x: &[u8]) -> $name {
+                let mut res = $name::zero();
+                raw_decoder(x, &mut res.value);
+                res
+            }
+        }
+    }
+}
+
+macro_rules! generate_encoder {
+    ($name: ident) => {
+        impl Encoder for $name {
+            fn to_bytes(&self) -> Vec<u8> {
+                let mut res = Vec::with_capacity(self.value.len() * 8);
+                for v in self.value.iter().rev() {
+                    let val = *v;
+                    res.push( (val >> 56) as u8);
+                    res.push( (val >> 48) as u8);
+                    res.push( (val >> 40) as u8);
+                    res.push( (val >> 32) as u8);
+                    res.push( (val >> 24) as u8);
+                    res.push( (val >> 16) as u8);
+                    res.push( (val >>  8) as u8);
+                    res.push( (val >>  0) as u8);
+                }
+                res
+            }
+        }
+    }
+}
+
+macro_rules! generate_codec
+{
+    ($name: ident) => {
+        generate_decoder!($name);
+        generate_encoder!($name);
+    }
+}

src/unsigned/conversion.rs

@@ -0,0 +1,83 @@
+macro_rules! generate_base_conversions
+{
+    ($name: ident) => {
+        generate_base_type_convert!($name, u8);
+        generate_base_type_convert!($name, u16);
+        generate_base_type_convert!($name, u32);
+        generate_base_type_convert!($name, u64);
+        generate_base_type_convert!($name, usize);
+
+        impl From<u128> for $name {
+            fn from(x: u128) -> $name {
+                let mut res = $name::zero();
+                res.value[0] = x as u64;
+                res.value[1] = (x >> 64) as u64;
+                res
+            }
+        }
+    };
+    () => {};
+}
+
+macro_rules! conversion_impls
+{
+    ($name: ident, $other: ident) => {
+        impl<'a> From<&'a $other> for $name {
+            fn from(x: &$other) -> $name {
+                let mut res = $name::zero();
+                let     len = res.value.len();
+                assert!(x.value.len() > res.value.len());
+                res.value.copy_from_slice(&x.value[0..len]);
+                res
+            }
+        }
+
+        impl<'a> From<&'a $name> for $other {
+            fn from(x: &$name) -> $other {
+                let mut res = $other::zero();
+                let     len = x.value.len();
+
+                assert!(x.value.len() < res.value.len());
+                res.value[0..len].copy_from_slice(&x.value);
+                res
+            }
+        }
+
+        impl From<$other> for $name {
+            fn from(x: $other) -> $name {
+                $name::from(&x)
+            }
+        }
+
+        impl From<$name> for $other {
+            fn from(x: $name) -> $other {
+                $other::from(&x)
+            }
+        }
+    };
+}
+
+macro_rules! generate_base_type_convert
+{
+    ($name: ident, $base: ident) => {
+        impl From<$base> for $name {
+            fn from(x: $base) -> $name {
+                let mut res = $name::zero();
+                res.value[0] = x as u64;
+                res
+            }
+        }
+
+        impl From<$name> for $base {
+            fn from(x: $name) -> $base {
+                x.value[0] as $base
+            }
+        }
+
+        impl<'a> From<&'a $name> for $base {
+            fn from(x: &$name) -> $base {
+                x.value[0] as $base
+            }
+        }
+    }
+}

src/unsigned/div.rs

@@ -0,0 +1,222 @@
+pub trait DivMod
+ where Self: Sized
+{
+    fn divmod(&self, rhs: &Self) -> (Self, Self);
+}
+
+pub fn get_number_size(v: &[u64]) -> Option<usize>
+{
+    for (idx, val) in v.iter().enumerate().rev() {
+        if *val != 0 {
+            return Some(idx);
+        }
+    }
+    None
+}
+
+macro_rules! safesubidx
+{
+    ($array: expr, $index: expr, $amt: expr) => ({
+        let idx = $index;
+        let amt = $amt;
+
+        if idx < amt {
+            0
+        } else {
+            $array[idx-amt]
+        }
+    })
+}
+
+macro_rules! div_impls
+{
+    ($name: ident, $dbl: ident) => {
+        impl DivMod for $name {
+            fn divmod(&self, rhs: &$name) -> ($name, $name) {
+                // if the divisor is larger, then the answer is pretty simple
+                if rhs > self {
+                    return ($name::zero(), self.clone());
+                }
+                // compute the basic number sizes
+                let mut n = match get_number_size(&self.value) {
+                                None    => 0,
+                                Some(v) => v
+                            };
+                let t = match get_number_size(&rhs.value) {
+                            None    => panic!("Division by zero!"),
+                            Some(v) => v
+                        };
+                assert!(t <= n);
+                // now generate mutable versions we can mess with
+                let mut x = $dbl::from(self);
+                let mut y = $dbl::from(rhs);
+                // If we want this to perform reasonable, it's useful if the
+                // value of y[t] is shifted so that the high bit is set.
+                let lambda_shift = y.value[t].leading_zeros() as usize;
+                if lambda_shift != 0 {
+                    let dupx = x.value.clone();
+                    let dupy = y.value.clone();
+
+                    shiftl(&mut x.value, &dupx, lambda_shift);
+                    shiftl(&mut y.value, &dupy, lambda_shift);
+                    n = get_number_size(&x.value).unwrap();
+                }
+                // now go!
+                // 1. For j from 0 to (n-t) do: q[j] = 0;
+                //      [NB: I take some liberties with this concept]
+                let mut q = $dbl::zero();
+                // 2. While (x >= y * b^(n-t)) do the following:
+                let mut ybnt = $dbl::zero();
+                for i in 0..self.value.len() {
+                    ybnt.value[(n-t)+i] = y.value[i];
+                    if (n-t)+i >= ybnt.value.len() {
+                        break;
+                    }
+                }
+                while x > ybnt {
+                    q.value[n - t] += 1;
+                    x -= &ybnt;
+                }
+                // 3. For i from n down to t+1 do the following:
+                let mut i = n;
+                while i >= (t + 1) {
+                    // 3.1. If x[i] = y[t]
+                    if x.value[i] == y.value[t] {
+                        // ... then set q[i-t-1] = b - 1
+                        q.value[i-t-1] = 0xFFFFFFFFFFFFFFFF;
+                    } else {
+                        // ... otherwise set q[i-t-1] =
+                        //        floor((x[i] * b + x[i-1]) / y[t])
+                        let xib         = (x.value[i] as u128) << 64;
+                        let xi1         = safesubidx!(x.value,i,1) as u128;
+                        let yt          = y.value[t] as u128;
+                        let qit1        = (xib + xi1) / yt;
+                        q.value[i-t-1] = qit1 as u64;
+                    }
+                    // 3.2. While q[i-t-1] * (y[t]*b + y[t-1]) >
+                    //                  (x[i] * b^2 + x[i-1] * b + x[i-2])
+                    loop {
+                        // three is very close to 2.
+                        let     qit1    = U192::from(safesubidx!(q.value,i-t,1));
+                        let mut ybits   = U192::zero();
+                        ybits.value[0]  = safesubidx!(y.value, t, 1);
+                        ybits.value[1]  = y.value[t];
+                        let       qiybs = &qit1 * &ybits;
+                        let mut   xbits = U384::zero();
+                        xbits.value[0]  = safesubidx!(x.value,i,2);
+                        xbits.value[1]  = safesubidx!(x.value,i,1);
+                        xbits.value[2]  = x.value[i];
+
+                        if !(&qiybs > &xbits) {
+                            break;
+                        }
+
+                        // ... do q[i-t-1] = q[i-t-1] - 1
+                        q.value[i-t-1] -= 1;
+                    }
+                    // 3.3. x = x - q[i-t-1] * y * b^(i-t-1)
+                    // 3.4. If x < 0
+                    //      then set x = x + y * b^(i-t-1) and
+                    //               q[i-t-1] = q[i-t-1] - 1
+                    let mut qbit1 = $name::zero();
+                    qbit1.value[i-t-1] = q.value[i-t-1];
+                    let smallery = $name::from(&y);
+                    let mut subpart = &smallery * &qbit1;
+                    if subpart > x {
+                        let mut addback = $dbl::zero();
+                        for (idx, val) in y.value.iter().enumerate() {
+                            let dest = idx + (i - t - 1);
+                            if dest < addback.value.len() {
+                                addback.value[dest] = *val;
+                            }
+                        }
+                        q.value[i-t-1] -= 1;
+                        subpart -= &addback;
+                    }
+                    assert!(subpart <= x);
+                    x -= &subpart;
+                    i -= 1;
+                }
+                // 4. r = x ... sort of. Remember, we potentially did a bit of shifting
+                // around at the very beginning, which we now need to account for. On the
+                // bright side, we only need to account for this in the remainder.
+                let mut r = $name::from(&x);
+                let dupr = r.value.clone();
+                shiftr(&mut r.value, &dupr, lambda_shift);
+                // 5. Return (q,r)
+                let resq = $name::from(&q);
+                (resq, r)
+            }
+        }
+        impl Div for $name {
+            type Output = $name;
+
+            fn div(self, rhs: $name) -> $name {
+                let (res, _) = self.divmod(&rhs);
+                res
+            }
+        }
+
+        impl<'a> Div<&'a $name> for $name {
+            type Output = $name;
+
+            fn div(self, rhs: &$name) -> $name {
+                let (res, _) = self.divmod(rhs);
+                res
+            }
+        }
+
+        impl<'a> Div<$name> for &'a $name {
+            type Output = $name;
+
+            fn div(self, rhs: $name) -> $name {
+                let (res, _) = self.divmod(&rhs);
+                res
+            }
+        }
+        impl<'a,'b> Div<&'a $name> for &'b $name {
+            type Output = $name;
+
+            fn div(self, rhs: &$name) -> $name {
+                let (res, _) = self.divmod(rhs);
+                res
+            }
+        }
+
+        impl Rem for $name {
+            type Output = $name;
+
+            fn rem(self, rhs: $name) -> $name {
+                let (_, res) = self.divmod(&rhs);
+                res
+            }
+        }
+
+        impl<'a> Rem<&'a $name> for $name {
+            type Output = $name;
+
+            fn rem(self, rhs: &$name) -> $name {
+                let (_, res) = self.divmod(&rhs);
+                res
+            }
+        }
+
+        impl<'a> Rem<$name> for &'a $name {
+            type Output = $name;
+
+            fn rem(self, rhs: $name) -> $name {
+                let (_, res) = self.divmod(&rhs);
+                res
+            }
+        }
+
+        impl<'a,'b> Rem<&'a $name> for &'b $name {
+            type Output = $name;
+
+            fn rem(self, rhs: &$name) -> $name {
+                let (_, res) = self.divmod(&rhs);
+                res
+            }
+        }
+    }
+}

src/unsigned/mod.rs

@@ -0,0 +1,63 @@
+#[macro_use]
+mod add;
+#[macro_use]
+mod barrett;
+#[macro_use]
+mod base;
+#[macro_use]
+mod cmp;
+#[macro_use]
+mod codec;
+#[macro_use]
+mod conversion;
+#[macro_use]
+mod div;
+#[macro_use]
+mod mul;
+#[macro_use]
+mod shifts;
+#[macro_use]
+mod sub;
+
+use self::add::{addition,unsafe_addition};
+use self::base::CryptoNum;
+use self::cmp::compare;
+use self::div::{DivMod,get_number_size};
+use self::codec::{Encoder,Decoder,raw_decoder};
+use self::mul::multiply;
+use self::shifts::{shiftl,shiftr};
+use self::sub::subtract;
+use std::cmp::{Ordering,min};
+use std::ops::{Add,AddAssign};
+use std::ops::{Div,Mul,Rem};
+use std::ops::{Shl,ShlAssign,Shr,ShrAssign};
+use std::ops::{Sub,SubAssign};
+
+#[cfg(test)]
+use std::fmt;
+
+macro_rules! generate_number
+{
+    ($name: ident, $size: expr) => {
+        generate_base!($name, $size);
+        generate_base_conversions!($name);
+        generate_codec!($name);
+
+        cmp_impls!($name);
+
+        subtraction_impls!($name, $size);
+        shift_impls!($name, $size);
+    };
+    ($name: ident, $size: expr, $plus1: ident, $times2: ident) => {
+        generate_number!($name, $size);
+        addition_impls!($name, $plus1);
+        multiply_impls!($name, $times2);
+        div_impls!($name, $times2);
+    };
+    ($name: ident, $size: expr, $plus1: ident, $times2: ident, $big: ident, $bar: ident) => {
+        generate_number!($name, $size, $plus1, $times2);
+        barrett_impl!($bar, $name, $plus1, $times2, $big);
+    }
+}
+
+include!("invoc.rs");

src/unsigned/mul.rs

@@ -0,0 +1,65 @@
+pub fn multiply(dest: &mut [u64], left: &[u64], right: &[u64])
+{
+    let len = right.len();
+
+    assert_eq!(left.len(), len,   "Uneven argument lengths in multiply");
+    assert_eq!(dest.len(), len*2, "Bad destination size in multiply");
+
+    for i in 0..len {
+        let mut carry = 0;
+
+        for j in 0..len {
+            let old = dest[i+j] as u128;
+            let l128 = left[j] as u128;
+            let r128 = right[i] as u128;
+            let uv = old + (l128 * r128) + carry;
+            dest[i+j] = uv as u64;
+            carry = uv >> 64;
+        }
+        dest[i+len] = carry as u64;
+    }
+}
+
+macro_rules! multiply_impls {
+    ($name: ident, $dbl: ident) => {
+        impl Mul<$name> for $name {
+            type Output = $dbl;
+
+            fn mul(self, rhs: $name) -> $dbl {
+                let mut res = $dbl::zero();
+                multiply(&mut res.value, &self.value, &rhs.value);
+                res
+            }
+        }
+
+        impl<'a> Mul<$name> for &'a $name {
+            type Output = $dbl;
+
+            fn mul(self, rhs: $name) -> $dbl {
+                let mut res = $dbl::zero();
+                multiply(&mut res.value, &self.value, &rhs.value);
+                res
+            }
+        }
+
+        impl<'a> Mul<&'a $name> for $name {
+            type Output = $dbl;
+
+            fn mul(self, rhs: &$name) -> $dbl {
+                let mut res = $dbl::zero();
+                multiply(&mut res.value, &self.value, &rhs.value);
+                res
+            }
+        }
+
+        impl<'a,'b> Mul<&'a $name> for &'b $name {
+            type Output = $dbl;
+
+            fn mul(self, rhs: &$name) -> $dbl {
+                let mut res = $dbl::zero();
+                multiply(&mut res.value, &self.value, &rhs.value);
+                res
+            }
+        }
+    };
+}

src/unsigned/shifts.rs

@@ -0,0 +1,92 @@
+pub(crate) fn shiftl(res: &mut [u64], copy: &[u64], amt: usize) {
+    let digits = amt / 64;
+    let bits   = amt % 64;
+
+    let mut carry = 0;
+    let     shift = 64 - bits;
+
+    for i in 0..res.len() {
+        let base = if i >= digits { copy[i-digits] } else { 0 };
+        let new_carry = if shift == 64 { 0 } else { base >> shift };
+        res[i] = (base << bits) | carry;
+        carry = new_carry;
+    }
+}
+
+pub(crate) fn shiftr(res: &mut [u64], copy: &[u64], amt: usize) {
+    let digits = amt / 64;
+    let bits   = amt % 64;
+
+    let mut carry = 0;
+    let mask = !(0xFFFFFFFFFFFFFFFF << bits);
+    let shift = (64 - bits) as u32;
+
+    for (idx, val) in res.iter_mut().enumerate().rev() {
+        let target = idx + digits;
+        let base = if target >= copy.len() { 0 } else { copy[target] };
+        let (new_carry, _) = (base & mask).overflowing_shl(shift);
+        *val = (base >> bits) | carry;
+        carry = new_carry;
+    }
+}
+
+macro_rules! shift_impls
+{
+    ($name: ident, $size: expr) => {
+        impl ShlAssign<usize> for $name {
+            fn shl_assign(&mut self, amt: usize) {
+                let copy = self.value.clone();
+                shiftl(&mut self.value, &copy, amt);
+            }
+        }
+
+        impl Shl<usize> for $name {
+            type Output = $name;
+
+            fn shl(mut self, amt: usize) -> $name {
+                let copy = self.value.clone();
+                shiftl(&mut self.value, &copy, amt);
+                self
+            }
+        }
+
+        impl<'a> Shl<usize> for &'a $name {
+            type Output = $name;
+
+            fn shl(self, amt: usize) -> $name {
+                let mut res = $name{ value: self.value.clone() };
+                shiftl(&mut res.value, &self.value, amt);
+                res
+            }
+        }
+
+        impl ShrAssign<usize> for $name {
+            fn shr_assign(&mut self, amt: usize) {
+                let copy = self.value.clone();
+                shiftr(&mut self.value, &copy, amt);
+            }
+        }
+
+        impl Shr<usize> for $name {
+            type Output = $name;
+
+            fn shr(mut self, amt: usize) -> $name {
+                let copy = self.value.clone();
+                shiftr(&mut self.value, &copy, amt);
+                self
+            }
+        }
+
+        impl<'a> Shr<usize> for &'a $name {
+            type Output = $name;
+
+            fn shr(self, amt: usize) -> $name {
+                let mut res = $name{ value: self.value.clone() };
+                shiftr(&mut res.value, &self.value, amt);
+                res
+            }
+        }
+    }
+}
+
+//shift_impls!(U192,   3);

src/unsigned/sub.rs

@@ -0,0 +1,76 @@
+use unsigned::add::unsafe_addition;
+
+pub fn subtract(res: &mut [u64], spare: &mut [u64], other: &[u64])
+{
+    for i in 0..res.len() {
+        res[i] = !res[i];
+    }
+    spare[0] = 1;
+    unsafe_addition(res, &spare);
+    unsafe_addition(res, &other);
+}
+
+macro_rules! subtraction_impls
+{
+    ($name: ident, $size: expr) => {
+        impl SubAssign for $name {
+            fn sub_assign(&mut self, rhs: $name) {
+                let mut temp = [0; $size];
+                subtract(&mut self.value, &mut temp, &rhs.value);
+            }
+        }
+
+        impl<'a> SubAssign<&'a $name> for $name {
+            fn sub_assign(&mut self, rhs: &$name) {
+                let mut temp = [0; $size];
+                subtract(&mut self.value, &mut temp, &rhs.value);
+            }
+        }
+
+        impl Sub for $name {
+            type Output = $name;
+
+            fn sub(self, rhs: $name) -> $name {
+                let mut res  = $name::zero();
+                let mut temp = [0; $size];
+                subtract(&mut res.value, &mut temp, &rhs.value);
+                res
+            }
+        }
+
+        impl<'a> Sub<$name> for &'a $name {
+            type Output = $name;
+
+            fn sub(self, rhs: $name) -> $name {
+                let mut res  = $name::zero();
+                let mut temp = [0; $size];
+                subtract(&mut res.value, &mut temp, &rhs.value);
+                res
+            }
+        }
+
+        impl<'a> Sub<&'a $name> for $name {
+            type Output = $name;
+
+            fn sub(self, rhs: &$name) -> $name {
+                let mut res  = $name::zero();
+                let mut temp = [0; $size];
+                subtract(&mut res.value, &mut temp, &rhs.value);
+                res
+            }
+        }
+
+        impl<'a,'b> Sub<&'a $name> for &'b $name {
+            type Output = $name;
+
+            fn sub(self, rhs: &$name) -> $name {
+                let mut res  = $name::zero();
+                let mut temp = [0; $size];
+                subtract(&mut res.value, &mut temp, &rhs.value);
+                res
+            }
+        }
+    }
+}
+
+//subtraction_impls!(U192,   3);