From 2b9f5ea7a2b03a39bd2de07a5c828986ea45a386 Mon Sep 17 00:00:00 2001 From: Adam Wick Date: Fri, 30 Nov 2018 11:28:20 -0800 Subject: [PATCH] Support unsigned integral square root computations. --- src/unsigned/invoc.rs | 17 + src/unsigned/mod.rs | 3 + src/unsigned/sqrt.rs | 66 + test-generator/Invocs.hs | 40 +- test-generator/Math.hs | 20 + test-generator/Requirements.hs | 9 +- test-generator/Tests.hs | 8 + testdata/sqrt/00192.test | 2002 +++++++++++++++++++++ testdata/sqrt/00256.test | 2002 +++++++++++++++++++++ testdata/sqrt/01024.test | 2002 +++++++++++++++++++++ testdata/sqrt/02048.test | 2002 +++++++++++++++++++++ testdata/sqrt/03072.test | 2002 +++++++++++++++++++++ testdata/sub/00192.test | 3003 ++++++++++++++++++++++++++++++++ 13 files changed, 13156 insertions(+), 20 deletions(-) create mode 100644 src/unsigned/sqrt.rs create mode 100644 testdata/sqrt/00192.test create mode 100644 testdata/sqrt/00256.test create mode 100644 testdata/sqrt/01024.test create mode 100644 testdata/sqrt/02048.test create mode 100644 testdata/sqrt/03072.test create mode 100644 testdata/sub/00192.test diff --git a/src/unsigned/invoc.rs b/src/unsigned/invoc.rs index 0d44037..ab390df 100644 --- a/src/unsigned/invoc.rs +++ b/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}; diff --git a/src/unsigned/mod.rs b/src/unsigned/mod.rs index 515a1b5..14790b1 100644 --- a/src/unsigned/mod.rs +++ b/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; diff --git a/src/unsigned/sqrt.rs b/src/unsigned/sqrt.rs new file mode 100644 index 0000000..c6865f6 --- /dev/null +++ b/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()); + }); + }; +} \ No newline at end of file diff --git a/test-generator/Invocs.hs b/test-generator/Invocs.hs index a8b2322..ad66bdc 100644 --- a/test-generator/Invocs.hs +++ b/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 "conversion" BaseOps False 90000 [] - generateTestBlock hndl "codec" BaseOps False 90000 [] - generateTestBlock hndl "cmp" BaseOps True 16384 [] - generateTestBlock hndl "sub" Sub True 9000 [] - generateTestBlock hndl "shiftl" Shifts True 9000 [] - generateTestBlock hndl "shiftr" Shifts True 9000 [] - generateTestBlock hndl "add" Add True 9000 [(+ 64)] - generateTestBlock hndl "mul" Mul True 9000 [(* 2)] - generateTestBlock hndl "div" Div True 2049 [] - generateTestBlock hndl "barrett_gen" Barretts True 2000 [(+ 64)] - generateTestBlock hndl "barrett_red" Barretts True 4000 [(+ 64), (* 2)] - generateTestBlock hndl "modsq" ModSq True 4000 [] - generateTestBlock hndl "modmul" ModMul True 4000 [] - generateTestBlock hndl "modexp" ModExp True 512 [] - generateTestBlock hndl "square" Square True 4000 [(* 2)] - generateTestBlock hndl "barrett_modsq" ModSq True 4000 [(+ 64)] - generateTestBlock hndl "barrett_modmul" ModMul True 4000 [(+ 64)] - generateTestBlock hndl "barrett_modexp" ModExp True 1024 [(+ 64)] + generateTestBlock hndl "base" BaseOps True 16384 [] + generateTestBlock hndl "conversion" BaseOps False 90000 [] + generateTestBlock hndl "codec" BaseOps False 90000 [] + generateTestBlock hndl "cmp" BaseOps True 16384 [] + generateTestBlock hndl "sub" Sub True 9000 [] + generateTestBlock hndl "shiftl" Shifts True 9000 [] + generateTestBlock hndl "shiftr" Shifts True 9000 [] + generateTestBlock hndl "add" Add True 9000 [(+ 64)] + generateTestBlock hndl "mul" Mul True 9000 [(* 2)] + generateTestBlock hndl "div" Div True 2049 [] + generateTestBlock hndl "barrett_gen" Barretts True 2000 [(+ 64)] + generateTestBlock hndl "barrett_red" Barretts True 4000 [(+ 64), (* 2)] + generateTestBlock hndl "modsq" ModSq True 4000 [] + generateTestBlock hndl "modmul" ModMul True 4000 [] + generateTestBlock hndl "modexp" ModExp True 512 [] + generateTestBlock hndl "square" Square True 4000 [(* 2)] + generateTestBlock hndl "sqrt" SquareRoot True 4096 [] + generateTestBlock hndl "barrett_modsq" ModSq True 4000 [(+ 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) -> diff --git a/test-generator/Math.hs b/test-generator/Math.hs index 9f1ae07..35a180e 100644 --- a/test-generator/Math.hs +++ b/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 diff --git a/test-generator/Requirements.hs b/test-generator/Requirements.hs index 317498b..26b0679 100644 --- a/test-generator/Requirements.hs +++ b/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] diff --git a/test-generator/Tests.hs b/test-generator/Tests.hs index 2f10a0c..f3f9b93 100644 --- a/test-generator/Tests.hs +++ b/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) diff --git a/testdata/sqrt/00192.test b/testdata/sqrt/00192.test new file mode 100644 index 0000000..671ca07 --- /dev/null +++ b/testdata/sqrt/00192.test @@ -0,0 +1,2002 @@ +a: ffffffffffffffffffffffffffffffffd8c9d194ae965286 +r: ffffffffffffffffffffffff +a: ffffffffffffffffffffffffffffffff82355eccfd5b6144 +r: ffffffffffffffffffffffff +a: 190836f566d1154a +r: 500d23a7 +a: 1d1ec627e8467da5 +r: 56574df6 +a: ffffffffffffffffffffffffffffffffa230f768410d562e +r: ffffffffffffffffffffffff +a: ffffffffffffffffffffffffffffffffdfccf0cd0d8e57ab +r: ffffffffffffffffffffffff +a: 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