Support unsigned integral square root computations.

src/unsigned/invoc.rs

@@ -3,9 +3,11 @@ base_impls!(U192, 3);
 random_impls!(U192, UniformU192);
 multiply_impls!(U192, U384);
 shift_impls!(U192, 3);
+subtraction_impls!(U192, 3);
 conversion_impls!(U192, U256);
 conversion_impls!(U192, U384);
 conversion_impls!(U192, U1024);
+sqrt_impls!(U192);
 addition_impls!(U256, U320);
 base_impls!(U256, 4);
 random_impls!(U256, UniformU256);
@@ -24,6 +26,7 @@ conversion_impls!(U256, U512);
 conversion_impls!(U256, U576);
 conversion_impls!(U256, U2048);
 conversion_impls!(U256, U3072);
+sqrt_impls!(U256);
 prime_gen_impls!(U256);
 addition_impls!(U320, U384);
 base_impls!(U320, 5);
@@ -92,6 +95,7 @@ subtraction_impls!(U1024, 16);
 conversion_impls!(U1024, U1088);
 conversion_impls!(U1024, U2048);
 conversion_impls!(U1024, U2112);
+sqrt_impls!(U1024);
 prime_gen_impls!(U1024);
 addition_impls!(U1088, U1152);
 base_impls!(U1088, 17);
@@ -152,6 +156,7 @@ subtraction_impls!(U2048, 32);
 conversion_impls!(U2048, U2112);
 conversion_impls!(U2048, U4096);
 conversion_impls!(U2048, U4160);
+sqrt_impls!(U2048);
 prime_gen_impls!(U2048);
 addition_impls!(U2112, U2176);
 base_impls!(U2112, 33);
@@ -184,6 +189,7 @@ subtraction_impls!(U3072, 48);
 conversion_impls!(U3072, U3136);
 conversion_impls!(U3072, U6144);
 conversion_impls!(U3072, U6208);
+sqrt_impls!(U3072);
 addition_impls!(U3136, U3200);
 base_impls!(U3136, 49);
 random_impls!(U3136, UniformU3136);
@@ -608,6 +614,7 @@ mod tests {
     use super::super::*;
     use testing::{build_test_path,run_test};
 
+    generate_sub_tests!(U192, u192);
     generate_sub_tests!(U256, u256);
     generate_sub_tests!(U320, u320);
     generate_sub_tests!(U512, u512);
@@ -901,6 +908,16 @@ mod tests {
     generate_square_tests!(ignore U8192, u8192, U16384);
     generate_square_tests!(ignore U15360, u15360, U30720);
   }
+  mod sqrt {
+    use super::super::*;
+    use testing::{build_test_path,run_test};
+
+    generate_sqrt_tests!(U192, u192);
+    generate_sqrt_tests!(U256, u256);
+    generate_sqrt_tests!(U1024, u1024);
+    generate_sqrt_tests!(U2048, u2048);
+    generate_sqrt_tests!(U3072, u3072);
+  }
   mod barrett_modsq {
     use super::super::*;
     use testing::{build_test_path,run_test};

src/unsigned/mod.rs

@@ -44,6 +44,8 @@ mod rand;
 #[macro_use]
 mod shifts;
 #[macro_use]
+mod sqrt;
+#[macro_use]
 mod square;
 #[macro_use]
 mod sub;
@@ -56,6 +58,7 @@ pub use self::modmul::ModMul;
 pub use self::modsq::ModSquare;
 pub use self::primes::PrimeGen;
 pub use self::square::Square;
+pub use self::sqrt::SquareRoot;
 
 pub(crate) use self::add::unsafe_addition;
 

src/unsigned/sqrt.rs

@@ -0,0 +1,66 @@
+pub trait SquareRoot {
+    /// Compute the integer square root of the given value. The integer square
+    /// root is the value Z such that the real root R satisfies Z <= R < Z+1.
+    fn sqrt(&self) -> Self;
+}
+
+macro_rules! sqrt_impls
+{
+    ($name: ident) => {
+        impl SquareRoot for $name {
+            fn sqrt(&self) -> Self {
+                let mut num = self.clone();
+                let mut res = $name::zero();
+                let mut bit = $name::from(1u64) << ($name::bit_length() - 2);
+
+                while bit > num {
+                    bit >>= 2;
+                }
+
+                while !bit.is_zero() {
+                    let mut resbit = res.clone();
+
+                    resbit += &bit;
+                    if num >= resbit {
+                        num -= resbit;
+                        res += &bit << 1;
+                    }
+
+                    res >>= 1;
+                    bit >>= 2;
+                }
+
+                res
+            }
+        }
+    }
+}
+
+#[cfg(test)]
+macro_rules! generate_sqrt_tests {
+    ($name: ident, $lname: ident) => {
+        #[test]
+        fn $lname() {
+            generate_sqrt_tests!(body $name, $lname);
+        }
+    };
+    (ignore $name: ident, $lname: ident) => {
+        #[test]
+        #[ignore]
+        fn $lname() {
+            generate_sqrt_tests!(body $name, $lname);
+        }
+    };
+    (body $name: ident, $lname: ident) => {
+        let fname = build_test_path("sqrt", stringify!($name));
+        run_test(fname.to_string(), 2, |case| {
+            let (neg0, abytes) = case.get("a").unwrap();
+            let (neg1, rbytes) = case.get("r").unwrap();
+            assert!(!neg0 && !neg1);
+
+            let a = $name::from_bytes(abytes);
+            let r = $name::from_bytes(rbytes);
+            assert_eq!(r, a.sqrt());
+        });
+    };
+}

test-generator/Invocs.hs

@@ -62,6 +62,7 @@ main = do
            Mul        -> hPutStrLn hndl ("multiply_impls!(U" ++ show size ++ ", U" ++ show (size * 2) ++ ");")
            Shifts     -> hPutStrLn hndl ("shift_impls!(U" ++ show size ++ ", " ++ show (size `div` 64) ++ ");")
            Square     -> hPutStrLn hndl ("square_impls!(U" ++ show size ++ ", U" ++ show (size * 2) ++ ", " ++ show size ++ ");")
+           SquareRoot -> hPutStrLn hndl ("sqrt_impls!(U" ++ show size ++ ");")
            Sub        -> hPutStrLn hndl ("subtraction_impls!(U" ++ show size ++ ", " ++ show (size `div` 64) ++ ");")
            Convert to -> hPutStrLn hndl ("conversion_impls!(U" ++ show size ++ ", U" ++ show to ++ ");")
            PrimeGen   -> hPutStrLn hndl ("prime_gen_impls!(U" ++ show size ++ ");")
@@ -69,25 +70,26 @@ main = do
        hPutStrLn hndl ""
        hPutStrLn hndl "\n#[cfg(test)]"
        hPutStrLn hndl "mod tests {"
-       generateTestBlock hndl "base"           BaseOps  True  16384 []
+       generateTestBlock hndl "base"           BaseOps    True  16384 []
-       generateTestBlock hndl "conversion"     BaseOps  False 90000 []
+       generateTestBlock hndl "conversion"     BaseOps    False 90000 []
-       generateTestBlock hndl "codec"          BaseOps  False 90000 []
+       generateTestBlock hndl "codec"          BaseOps    False 90000 []
-       generateTestBlock hndl "cmp"            BaseOps  True  16384 []
+       generateTestBlock hndl "cmp"            BaseOps    True  16384 []
-       generateTestBlock hndl "sub"            Sub      True  9000  []
+       generateTestBlock hndl "sub"            Sub        True  9000  []
-       generateTestBlock hndl "shiftl"         Shifts   True  9000  []
+       generateTestBlock hndl "shiftl"         Shifts     True  9000  []
-       generateTestBlock hndl "shiftr"         Shifts   True  9000  []
+       generateTestBlock hndl "shiftr"         Shifts     True  9000  []
-       generateTestBlock hndl "add"            Add      True  9000  [(+ 64)]
+       generateTestBlock hndl "add"            Add        True  9000  [(+ 64)]
-       generateTestBlock hndl "mul"            Mul      True  9000  [(* 2)]
+       generateTestBlock hndl "mul"            Mul        True  9000  [(* 2)]
-       generateTestBlock hndl "div"            Div      True  2049  []
+       generateTestBlock hndl "div"            Div        True  2049  []
-       generateTestBlock hndl "barrett_gen"    Barretts True  2000  [(+ 64)]
+       generateTestBlock hndl "barrett_gen"    Barretts   True  2000  [(+ 64)]
-       generateTestBlock hndl "barrett_red"    Barretts True  4000  [(+ 64), (* 2)]
+       generateTestBlock hndl "barrett_red"    Barretts   True  4000  [(+ 64), (* 2)]
-       generateTestBlock hndl "modsq"          ModSq    True  4000  []
+       generateTestBlock hndl "modsq"          ModSq      True  4000  []
-       generateTestBlock hndl "modmul"         ModMul   True  4000  []
+       generateTestBlock hndl "modmul"         ModMul     True  4000  []
-       generateTestBlock hndl "modexp"         ModExp   True  512   []
+       generateTestBlock hndl "modexp"         ModExp     True  512   []
-       generateTestBlock hndl "square"         Square   True  4000  [(* 2)]
+       generateTestBlock hndl "square"         Square     True  4000  [(* 2)]
-       generateTestBlock hndl "barrett_modsq"  ModSq    True  4000  [(+ 64)]
+       generateTestBlock hndl "sqrt"           SquareRoot True  4096  []
-       generateTestBlock hndl "barrett_modmul" ModMul   True  4000  [(+ 64)]
+       generateTestBlock hndl "barrett_modsq"  ModSq      True  4000  [(+ 64)]
-       generateTestBlock hndl "barrett_modexp" ModExp   True  1024  [(+ 64)]
+       generateTestBlock hndl "barrett_modmul" ModMul     True  4000  [(+ 64)]
+       generateTestBlock hndl "barrett_modexp" ModExp     True  1024  [(+ 64)]
        hPutStrLn hndl "}"
   withFile "../src/signed/invoc.rs" WriteMode $ \ hndl ->
     do forM_ requirements $ \ (Req size oper) ->

test-generator/Math.hs

@@ -3,10 +3,12 @@ module Math(
          extendedGCD
        , barrett, computeK, base
        , modulate, modulate'
+       , isqrt
        , showX, showB
        )
  where
 
+import Data.Bits(shiftL,shiftR)
 import Numeric(showHex)
 
 data AlgState = AlgState {
@@ -102,6 +104,24 @@ showB :: Bool -> String
 showB False = "0"
 showB True  = "1"
 
+isqrt :: Int -> Integer -> Integer
+isqrt bits val = final
+  where
+   bit' = part1 (1 `shiftL` (bits - 2))
+   --
+   part1 x | x > val   = part1 (x `shiftR` 2)
+           | otherwise = x
+   --
+   final = loop val 0 bit'
+   --
+   loop num res bit
+     | bit == 0 = res
+     | otherwise = let (num', res') = adjust num res bit
+                   in loop num' (res' `shiftR` 1) (bit `shiftR` 2)
+   adjust num res bit
+     | num >= (res + bit) = (num - (res + bit), res + (bit `shiftL` 1))
+     | otherwise          = (num, res)
+
 _run :: Integer -> Integer -> IO ()
 _run inputx inputy =
   do let (x, y, g, initState) = initialState inputx inputy 1

test-generator/Requirements.hs

@@ -25,6 +25,7 @@ data Operation = Add
                | SignedShift
                | SignedSub
                | SigConvert Int
+               | SquareRoot
                | EGCD
                | ModInv
                | PrimeGen
@@ -47,7 +48,8 @@ needs = [ Need RSA         (\ size -> [Req (size `div` 2) Sub,
                                       ])
         , Need DSA         (\ size -> [Req size BaseOps,
                                        Req size Shifts,
-                                       Req size Add])
+                                       Req size Add,
+                                       Req size SquareRoot])
         , Need PrimeGen    (\ size -> [Req size Div,
                                        Req size Shifts,
                                        Req size ModExp,
@@ -149,6 +151,11 @@ needs = [ Need RSA         (\ size -> [Req (size `div` 2) Sub,
                                        Req (size + 64) SignedAdd,
                                        Req size Barretts
                                       ])
+        , Need SquareRoot  (\ size -> [Req size BaseOps,
+                                       Req size Shifts,
+                                       Req size Add,
+                                       Req size Sub
+                                      ])
         ]
 
 newRequirements :: Requirement -> [Requirement]

test-generator/Tests.hs

@@ -39,6 +39,7 @@ testDatabase = [
     (SignedShift, "sigshiftr",      "signed shift right",      sigshiftrTest),
     (SignedShift, "sigshiftl",      "signed shift left",       sigshiftlTest),
     (SignedSub,   "sigsub",         "signed subtraction",      sigsubTest),
+    (SquareRoot,  "sqrt",           "square root",             sqrtTest),
     (EGCD,        "egcd",           "EGCD",                    egcdTest),
     (ModInv,      "modinv",         "modular inversion",       modinvTest)
   ]
@@ -202,6 +203,13 @@ sigsubTest size memory0 =
                                    ("c", showX c)]
   in (res, c, memory2)
 
+sqrtTest :: Test
+sqrtTest size memory0 =
+  let (a, memory1) = generateNum memory0 "a" size
+      r            = isqrt size a
+      res          = Map.fromList [("a", showX a), ("r", showX r)]
+  in (res, r, memory1)
+
 signedTest :: Test
 signedTest size memory0 =
   let (x, memory1) = genSign (generateNum memory0 "x" size)