diff --git a/src/cryptonum/conversions.rs b/src/cryptonum/conversions.rs index ea579c8..9fbf6da 100644 --- a/src/cryptonum/conversions.rs +++ b/src/cryptonum/conversions.rs @@ -13,6 +13,25 @@ macro_rules! define_from } } +macro_rules! define_signed_from +{ + ($type: ident, $base: ident, $uns: ident) => { + impl From<$uns> for $type { + fn from(x: $uns) -> $type { + SCN{ negative: false, value: UCN::from(x) } + } + } + + impl From<$base> for $type { + fn from(x: $base) -> $type { + let neg = x < 0; + let absx = x.abs(); + SCN{ negative: neg, value: UCN::from(absx as $uns) } + } + } + } +} + macro_rules! define_into { ($type: ident, $base: ident) => { @@ -27,3 +46,22 @@ macro_rules! define_into } } } + +macro_rules! define_signed_into +{ + ($type: ident, $base: ident, $uns: ident) => { + impl Into<$uns> for $type { + fn into(self) -> $uns { + let res: $uns = self.value.into(); + if self.negative { 0-res } else { res } + } + } + + impl Into<$base> for $type { + fn into(self) -> $base { + let res: $uns = self.value.into(); + if self.negative { (0-res) as $base } else { res as $base } + } + } + } +} diff --git a/src/cryptonum/mod.rs b/src/cryptonum/mod.rs index 1c6e3e2..c570101 100644 --- a/src/cryptonum/mod.rs +++ b/src/cryptonum/mod.rs @@ -2,1051 +2,8 @@ mod conversions; #[macro_use] mod complete_arith; +mod signed; +mod unsigned; -use num::{BigUint,ToPrimitive,Zero}; -use std::fmt; -use std::fmt::Write; -use std::cmp::Ordering; -use std::ops::*; - -/// In case you were wondering, it stands for "Unsigned Crypto Num". -#[derive(Clone,Debug,PartialEq,Eq)] -pub struct UCN { - contents: Vec -} - -impl UCN { - fn clean(&mut self) { - loop { - match self.contents.pop() { - None => - break, - Some(0) => - continue, - Some(x) => { - self.contents.push(x); - break - } - } - } - } - - fn expand(&mut self, rhs: &UCN) { - while self.contents.len() < rhs.contents.len() { - self.contents.push(0); - } - } - - pub fn from_str(x: &str) -> UCN { - let mut outvec = Vec::new(); - let mut worker = 0; - let mut shift = 0; - - for c in x.chars().rev() { - match c.to_digit(16) { - None => - panic!("Bad character in string!"), - Some(v) => { - worker = worker + ((v as u64) << shift); - shift += 4; - } - } - if shift == 64 { - outvec.push(worker); - worker = 0; - shift = 0; - } - } - outvec.push(worker); - let mut res = UCN{ contents: outvec }; - res.clean(); - res - } -} - - -impl fmt::UpperHex for UCN { - fn fmt(&self, fmt: &mut fmt::Formatter) -> Result<(),fmt::Error> { - for x in self.contents.iter().rev() { - fmt.write_char(tochar_upper(x >> 60))?; - fmt.write_char(tochar_upper(x >> 56))?; - fmt.write_char(tochar_upper(x >> 52))?; - fmt.write_char(tochar_upper(x >> 48))?; - fmt.write_char(tochar_upper(x >> 44))?; - fmt.write_char(tochar_upper(x >> 40))?; - fmt.write_char(tochar_upper(x >> 36))?; - fmt.write_char(tochar_upper(x >> 32))?; - fmt.write_char(tochar_upper(x >> 28))?; - fmt.write_char(tochar_upper(x >> 24))?; - fmt.write_char(tochar_upper(x >> 20))?; - fmt.write_char(tochar_upper(x >> 16))?; - fmt.write_char(tochar_upper(x >> 12))?; - fmt.write_char(tochar_upper(x >> 8))?; - fmt.write_char(tochar_upper(x >> 4))?; - fmt.write_char(tochar_upper(x >> 0))?; - } - Ok(()) - } -} - -fn tochar_upper(x: u64) -> char { - match (x as u8) & (0xF as u8) { - 0x0 => '0', - 0x1 => '1', - 0x2 => '2', - 0x3 => '3', - 0x4 => '4', - 0x5 => '5', - 0x6 => '6', - 0x7 => '7', - 0x8 => '8', - 0x9 => '9', - 0xA => 'A', - 0xB => 'B', - 0xC => 'C', - 0xD => 'D', - 0xE => 'E', - 0xF => 'F', - _ => panic!("the world is broken") - } -} - -impl fmt::LowerHex for UCN { - fn fmt(&self, fmt: &mut fmt::Formatter) -> Result<(),fmt::Error> { - for x in self.contents.iter().rev() { - fmt.write_char(tochar_lower(x >> 60))?; - fmt.write_char(tochar_lower(x >> 56))?; - fmt.write_char(tochar_lower(x >> 52))?; - fmt.write_char(tochar_lower(x >> 48))?; - fmt.write_char(tochar_lower(x >> 44))?; - fmt.write_char(tochar_lower(x >> 40))?; - fmt.write_char(tochar_lower(x >> 36))?; - fmt.write_char(tochar_lower(x >> 32))?; - fmt.write_char(tochar_lower(x >> 28))?; - fmt.write_char(tochar_lower(x >> 24))?; - fmt.write_char(tochar_lower(x >> 20))?; - fmt.write_char(tochar_lower(x >> 16))?; - fmt.write_char(tochar_lower(x >> 12))?; - fmt.write_char(tochar_lower(x >> 8))?; - fmt.write_char(tochar_lower(x >> 4))?; - fmt.write_char(tochar_lower(x >> 0))?; - } - Ok(()) - } -} - -fn tochar_lower(x: u64) -> char { - match (x as u8) & (0xF as u8) { - 0x0 => '0', - 0x1 => '1', - 0x2 => '2', - 0x3 => '3', - 0x4 => '4', - 0x5 => '5', - 0x6 => '6', - 0x7 => '7', - 0x8 => '8', - 0x9 => '9', - 0xA => 'a', - 0xB => 'b', - 0xC => 'c', - 0xD => 'd', - 0xE => 'e', - 0xF => 'f', - _ => panic!("the world is broken") - } -} - -//------------------------------------------------------------------------------ -// -// Conversions to/from crypto nums. -// -//------------------------------------------------------------------------------ - -define_from!(UCN, u8); -define_from!(UCN, u16); -define_from!(UCN, u32); -define_from!(UCN, u64); -define_into!(UCN, u8); -define_into!(UCN, u16); -define_into!(UCN, u32); -define_into!(UCN, u64); - -impl From for UCN { - fn from(mut x: BigUint) -> UCN { - let mut dest = Vec::new(); - let mask = BigUint::from(0xFFFFFFFFFFFFFFFF as u64); - - while !x.is_zero() { - match (&x & &mask).to_u64() { - None => - panic!("Can't use BigUint in From"), - Some(val) => - dest.push(val) - } - x >>= 64; - } - - UCN{ contents: dest } - } -} - -impl Into for UCN { - fn into(self) -> BigUint { - let mut result = BigUint::zero(); - - for part in self.contents.iter().rev() { - result <<= 64; - result += BigUint::from(*part); - } - - result - } -} - -//------------------------------------------------------------------------------ -// -// Comparisons -// -//------------------------------------------------------------------------------ - -impl PartialOrd for UCN { - fn partial_cmp(&self, other: &UCN) -> Option { - Some(self.cmp(other)) - } -} - -impl Ord for UCN { - fn cmp(&self, other: &UCN) -> Ordering { - match self.contents.len().cmp(&other.contents.len()) { - Ordering::Equal => { - let mut me = self.contents.iter().rev(); - let mut them = other.contents.iter().rev(); - - for (m, t) in me.zip(them) { - match m.cmp(t) { - Ordering::Equal => - continue, - res => - return res - } - } - - Ordering::Equal - } - x => x - } - } -} - -//------------------------------------------------------------------------------ -// -// Bit Operations -// -//------------------------------------------------------------------------------ - -impl Not for UCN { - type Output = UCN; - - fn not(self) -> UCN { - let mut contents = self.contents; - - for x in contents.iter_mut() { - *x = !*x; - } - - let mut res = UCN{ contents: contents }; - res.clean(); - res - } -} - -impl<'a> Not for &'a UCN { - type Output = UCN; - - fn not(self) -> UCN { - let res = self.clone(); - res.not() - } -} - -impl<'a> BitOrAssign<&'a UCN> for UCN { - fn bitor_assign(&mut self, rhs: &UCN) { - self.expand(&rhs); - { - let mut iter_me = self.contents.iter_mut(); - let mut iter_tm = rhs.contents.iter(); - - loop { - match (iter_me.next(), iter_tm.next()) { - (Some(dest), Some(val)) => - *dest |= val, - _ => - break - } - } - } - self.clean(); - } -} - -impl<'a> BitXorAssign<&'a UCN> for UCN { - fn bitxor_assign(&mut self, rhs: &UCN) { - self.expand(&rhs); - { - let mut iter_me = self.contents.iter_mut(); - let mut iter_tm = rhs.contents.iter(); - - loop { - match (iter_me.next(), iter_tm.next()) { - (Some(dest), Some(val)) => - *dest ^= val, - _ => - break - } - } - } - self.clean(); - } -} - -impl<'a> BitAndAssign<&'a UCN> for UCN { - fn bitand_assign(&mut self, rhs: &UCN) { - if self.contents.len() > rhs.contents.len() { - self.contents.resize(rhs.contents.len(), 0); - } - { - let mut iter_me = self.contents.iter_mut(); - let mut iter_tm = rhs.contents.iter(); - - loop { - match (iter_me.next(), iter_tm.next()) { - (Some(dest), Some(val)) => - *dest &= val, - _ => - break - } - } - } - self.clean(); - } -} - -derive_arithmetic_operators!(UCN, BitOr, bitor, BitOrAssign, bitor_assign); -derive_arithmetic_operators!(UCN, BitXor, bitxor, BitXorAssign, bitxor_assign); -derive_arithmetic_operators!(UCN, BitAnd, bitand, BitAndAssign, bitand_assign); - -//------------------------------------------------------------------------------ -// -// Shifts -// -//------------------------------------------------------------------------------ - -impl ShlAssign for UCN { - fn shl_assign(&mut self, rhs: u64) { - let mut digits = rhs / 64; - let bits = rhs % 64; - let mut carry = 0; - - // ripple the bit-level shift through - if bits != 0 { - for x in self.contents.iter_mut() { - let new_carry = *x >> (64 - bits); - *x = (*x << bits) | carry; - carry = new_carry; - } - } - - // if we pulled some stuff off the end, add it back - if carry != 0 { - self.contents.push(carry); - } - - // add the appropriate digits on the low side - while digits > 0 { - self.contents.insert(0,0); - digits -= 1; - } - } -} - -impl Shl for UCN { - type Output = UCN; - - fn shl(self, rhs: u64) -> UCN { - let mut copy = self.clone(); - copy.shl_assign(rhs); - copy - } -} - -derive_shift_operators!(UCN, ShlAssign, Shl, shl_assign, shl, usize); -derive_shift_operators!(UCN, ShlAssign, Shl, shl_assign, shl, u32); -derive_shift_operators!(UCN, ShlAssign, Shl, shl_assign, shl, u16); -derive_shift_operators!(UCN, ShlAssign, Shl, shl_assign, shl, u8); - -impl ShrAssign for UCN { - fn shr_assign(&mut self, rhs: u64) { - let mut digits = rhs / 64; - let bits = rhs % 64; - - // remove the appropriate digits on the low side - while digits > 0 { - self.contents.remove(0); - digits -= 1; - } - // ripple the shifts over - let mut carry = 0; - let mask = !(0xFFFFFFFFFFFFFFFF << bits); - - for x in self.contents.iter_mut().rev() { - let base = *x >> bits; - let (new_carry, _) = (*x & mask).overflowing_shl((64-bits) as u32); - *x = base | carry; - carry = new_carry; - } - // in this case, we just junk the extra carry bits, but we do need to - // cleanup possible zeros at the end. - self.clean(); - } -} - -impl Shr for UCN { - type Output = UCN; - - fn shr(self, rhs: u64) -> UCN { - let mut copy = self.clone(); - copy.shr_assign(rhs); - copy - } -} - -derive_shift_operators!(UCN, ShrAssign, Shr, shr_assign, shr, usize); -derive_shift_operators!(UCN, ShrAssign, Shr, shr_assign, shr, u32); -derive_shift_operators!(UCN, ShrAssign, Shr, shr_assign, shr, u16); -derive_shift_operators!(UCN, ShrAssign, Shr, shr_assign, shr, u8); - -derive_signed_shift_operators!(UCN, usize, isize); -derive_signed_shift_operators!(UCN, u64, i64); -derive_signed_shift_operators!(UCN, u32, i32); -derive_signed_shift_operators!(UCN, u16, i16); -derive_signed_shift_operators!(UCN, u8, i8); - -//------------------------------------------------------------------------------ -// -// Addition, Subtraction and Multiplication -// -//------------------------------------------------------------------------------ - -impl<'a> AddAssign<&'a UCN> for UCN { - fn add_assign(&mut self, rhs: &UCN) { - let mut iter_tm = rhs.contents.iter(); - let mut stolen = None; - let mut carry = 0; - - // loop through every element on the left hand side, breaking early - // on if we right the end of the left hand side. - { - let mut iter_me = self.contents.iter_mut(); - loop { - match(iter_me.next(), iter_tm.next()) { - (None, None) => - break, - (Some(dest), None) => { - let dest128 = *dest as u128; - let newdest = dest128 + carry; - *dest = newdest as u64; - carry = newdest >> 64; - } - (None, Some(x)) => { - stolen = Some(*x); - break; - } - (Some(dest), Some(r)) => { - let newdest = (*dest as u128) + (*r as u128) + carry; - *dest = newdest as u64; - carry = newdest >> 64; - } - } - } - } - // if we accidentally stole something form the right iterator, - // push it back on. - if let Some(x) = stolen { - let stolen128 = (x as u128) + carry; - self.contents.push(stolen128 as u64); - carry = stolen128 >> 64; - } - // now loop through any remaining items on the right hand side, - // pushing them onto the result. - for x in iter_tm { - let x128 = (*x as u128) + carry; - self.contents.push(x128 as u64); - carry = x128 >> 64; - } - // finally, if there's still a carry, push it on the end. - if carry > 0 { - self.contents.push(carry as u64); - } - } -} - -impl<'a> SubAssign<&'a UCN> for UCN { - fn sub_assign(&mut self, rhs: &UCN) { - { - let mut borrow = 0; - let mut iter_me = self.contents.iter_mut(); - let mut iter_tm = rhs.contents.iter(); - - loop { - assert!( (borrow == 0) | (borrow == 1) ); - match (iter_me.next(), iter_tm.next()) { - (None, None) if borrow == 0 => - break, - (None, None) => - panic!("Generated negative UCN in subtraction (1)."), - (Some(x), None) => { - if borrow == 0 { - break; - } - if *x == 0 { - *x = 0xFFFFFFFFFFFFFFFF; - borrow = 1; - } else { - *x = *x - borrow; - break; - } - } - (None, Some(_)) => { - panic!("Generated negative UCN in subtraction (2)."); - } - (Some(x), Some(y)) => { - if (*x - borrow) >= *y { - *x = (*x - borrow) - *y; - borrow = 0; - } else { - let x128 = (*x as u128) + 0x10000000000000000; - let res = x128 - (*y as u128) - (borrow as u128); - *x = res as u64; - borrow = 1; - } - } - } - } - } - self.clean(); - } -} - -impl<'a> MulAssign<&'a UCN> for UCN { - fn mul_assign(&mut self, rhs: &UCN) { - // Handle the quick and easy multiplication by zero cases first. - if self.contents.len() == 0 { - return; - } - if rhs.contents.len() == 0 { - self.contents.resize(0,0); - return; - } - - // OK, do some real multiplication - let x = self.contents.clone(); - let y = rhs.contents.clone(); - let outlen = x.len() + y.len(); - let n = y.len() - 1; - - // this algorithm is 14.12 from "Handbook of Applied Cryptography" - self.contents.resize(0, 0); - self.contents.resize(outlen, 0); - for (i,xi) in x.iter().enumerate() { - let mut c = 0; - for (j,yj) in y.iter().enumerate() { - let wij = self.contents[i+j] as u128; - let xjyi = (*xi as u128) * (*yj as u128); - let uv = wij + xjyi + c; - self.contents[i+j] = uv as u64; - c = uv >> 64; - } - self.contents[i+n+1] = c as u64; - } - self.clean(); - } -} - -fn divmod(quotient: &mut Vec, remainder: &mut Vec, - inx: &Vec, iny: &Vec) -{ - quotient.resize(0,0); - remainder.resize(0,0); - // This algorithm is 14.20 from "Handbook of Applied Cryptography" - // - // It requires that y[t] is not zero, which it isn't due to our invariant - // that we don't have unnecessary zeros at the end of the array. We note - // that it's also very convienent if the top bit of y[t] is set, as well, - // so we shift everything left so that things work out. - let mut xbuffer = Vec::with_capacity(inx.len() + 2); - let mut ybuffer = Vec::with_capacity(iny.len() + 2); - xbuffer.extend_from_slice(&inx); - ybuffer.extend_from_slice(&iny); - let mut x = UCN{ contents: xbuffer }; - let mut y = UCN{ contents: ybuffer }; - let additional_shift = iny[iny.len() - 1].leading_zeros() as usize; - x <<= additional_shift; - y <<= additional_shift; - // Once we've done this, we should be good to go with our mostly-correct - // x and y. The only trick is that the algorithm requires that n >= t. If - // this is not true, then the answer is zero, because the divisor is greater - // than the dividend. - let n = x.contents.len(); - let t = y.contents.len(); - if n < t { - remainder.extend_from_slice(&inx); - return; - } - // Also, it's real convient for n and t to be greater than one, which we - // achieve by pushing a zero into the low digit. Because we do this, we - // don't have to do a lot of testing against negative indices later. - x.contents.insert(0,0); - y.contents.insert(0,0); - // 1. For j from 0 to (n-t) do: qj <- 0. - let mut q = Vec::with_capacity(n - t + 1); - q.resize(n - t + 1, 0); - // 2. While (x >= yb^(n-t)) do the following: - // q_(n-t) <- q_(n-t) + 1 - // x <- x - yb^(n-t) - let ybnt = &y << (64 * (n - t)); - while &x >= &ybnt { - q[n-t] = q[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 xi = yt, then set q_(i-t-1) <- b - 1; otherwise set - // q_(i-t-1) <- floor((x_i * b + x_(i-1)) /y_t). - if x.contents[i] == y.contents[t] { - q[i-t-1] = 0xFFFFFFFFFFFFFFFF; - } else { - let top = ((x.contents[i] as u128)<<64) + (x.contents[i-1] as u128); - let bot = y.contents[t] as u128; - let solution = top / bot; - q[i-t-1] = solution as u64; - } - // 3.2. While (q_(i-t-1)(y_t * b + y_(t-1)) > x_i(b2) + x_(i-1)b + - // x_(i-2)) do: - // q_(i - t - 1) <- q_(i - t 1) - 1. - loop { - let qit1 = UCN{ contents: vec![q[i - t - 1]] }; - let ytbyt1 = UCN{ contents: vec![y.contents[t-1], y.contents[t]] }; - let left = qit1 * ytbyt1; - let right = UCN{ contents: vec![x.contents[i-2], - x.contents[i-1], - x.contents[i]] }; - - if left <= right { - break - } - - q[i - t - 1] -= 1; - } - // 3.3. x <- x - q_(i - t - 1) * y * b^(i-t-1) - let qit1 = UCN{ contents: vec![q[i - t - 1]] }; - let ybit1 = &y << (64 * (i - t - 1)); - let subbit = &qit1 * &ybit1; - if subbit <= x { - x -= subbit; - } else { - // 3.4. if x < 0 then set z <- x + yb^(i-t-1) and - // q_(i-t-1) <- q(i-t-1) - 1 - x -= subbit - ybit1; - q[i - t - 1] -= 1; - } - i -= 1; - } - // 4. r <- x - x >>= additional_shift; - if x.contents.len() > 0 { - // remember, we added a zero to the front of - // everything earlier; this removes it. - x.contents.remove(0); - } - remainder.append(&mut x.contents); - // 5. return (q,r) - while (q.len() > 0) && (q[q.len() - 1] == 0) { - q.pop(); - } - quotient.append(&mut q); -} - -impl<'a> DivAssign<&'a UCN> for UCN { - fn div_assign(&mut self, rhs: &UCN) { - let copy = self.contents.clone(); - let mut dead = Vec::new(); - divmod(&mut self.contents, &mut dead, ©, &rhs.contents); - } -} - -impl<'a> RemAssign<&'a UCN> for UCN { - fn rem_assign(&mut self, rhs: &UCN) { - let copy = self.contents.clone(); - let mut dead = Vec::new(); - divmod(&mut dead, &mut self.contents, ©, &rhs.contents); - } -} - -derive_arithmetic_operators!(UCN, Add, add, AddAssign, add_assign); -derive_arithmetic_operators!(UCN, Sub, sub, SubAssign, sub_assign); -derive_arithmetic_operators!(UCN, Mul, mul, MulAssign, mul_assign); -derive_arithmetic_operators!(UCN, Div, div, DivAssign, div_assign); -derive_arithmetic_operators!(UCN, Rem, rem, RemAssign, rem_assign); - -//------------------------------------------------------------------------------ -// -// Tests! -// -//------------------------------------------------------------------------------ - -#[cfg(test)] -mod test { - use quickcheck::{Arbitrary,Gen}; - use std::fs::File; - use std::io::Read; - use super::*; - - #[test] - fn test_clean() { - let mut val1 = UCN{ contents: vec![1,0,0] }; - val1.clean(); - assert_eq!(val1, UCN{ contents: vec![1] }); - // - let mut val2 = UCN{ contents: vec![0,0,0] }; - val2.clean(); - assert_eq!(val2, UCN{ contents: vec![] }); - // - let mut val3 = UCN{ contents: vec![1,0,1] }; - val3.clean(); - assert_eq!(val3, UCN{ contents: vec![1,0,1] }); - // - let mut val4 = UCN{ contents: vec![] }; - val4.clean(); - assert_eq!(val4, UCN{ contents: vec![] }); - } - - #[test] - #[allow(overflowing_literals)] - fn test_builders() { - assert_eq!(UCN{ contents: vec![] }, - UCN::from(0 as u8)); - assert_eq!(UCN{ contents: vec![0x7F] }, - UCN::from(0x7F as u8)); - assert_eq!(UCN{ contents: vec![0x7F7F] }, - UCN::from(0x7F7F as u16)); - assert_eq!(UCN{ contents: vec![0xCA5CADE5] }, - UCN::from(0xCA5CADE5 as u32)); - assert_eq!(UCN{ contents: vec![0xFFFFFFFFFFFFFFFF] }, - UCN::from(0xFFFFFFFFFFFFFFFF as u64)); - assert_eq!(UCN{ contents: vec![0x00000000FFFFFFFF] }, - UCN::from(0xFFFFFFFFFFFFFFFF as u32)); - } - - quickcheck! { - fn builder_u8_upgrade_u16(x: u8) -> bool { - UCN::from(x) == UCN::from(x as u16) - } - fn builder_u16_upgrade_u32(x: u16) -> bool { - UCN::from(x) == UCN::from(x as u32) - } - fn builder_u32_upgrade_u64(x: u32) -> bool { - UCN::from(x) == UCN::from(x as u64) - } - fn builder_u8_roundtrips(x: u8) -> bool { - let thereback: u8 = UCN::from(x).into(); - x == thereback - } - fn builder_u16_roundtrips(x: u16) -> bool { - let thereback: u16 = UCN::from(x).into(); - x == thereback - } - fn builder_u32_roundtrips(x: u32) -> bool { - let thereback: u32 = UCN::from(x).into(); - x == thereback - } - fn builder_u64_roundtrips(x: u64) -> bool { - let thereback: u64 = UCN::from(x).into(); - x == thereback - } - } - - quickcheck! { - fn u64_comparison_sane(x: u64, y: u64) -> bool { - let ucnx = UCN::from(x); - let ucny = UCN::from(y); - ucnx.cmp(&ucny) == x.cmp(&y) - } - fn longer_is_greater(x: u64, y: u64) -> bool { - if x == 0 { - true - } else { - let ucnx = UCN{ contents: vec![x, 1] }; - let ucny = UCN::from(y); - ucnx.cmp(&ucny) == Ordering::Greater - } - } - fn self_is_equal(x: Vec) -> bool { - let val = UCN{ contents: x }; - let copy = val.clone(); - - (&val == ©) && (val.cmp(©) == Ordering::Equal) - } - } - - impl Arbitrary for UCN { - fn arbitrary(g: &mut G) -> UCN { - let lenopts = [4,8,16,32,48,64,112,128,240]; - let mut len = *g.choose(&lenopts).unwrap(); - let mut contents = Vec::with_capacity(len); - - while len > 0 { - contents.push(g.gen()); - len -= 1; - } - UCN{ contents: contents } - } - } - - fn expand_to_match(a: &mut UCN, b: &UCN) { - assert!(a.contents.len() <= b.contents.len()); - while a.contents.len() < b.contents.len() { - a.contents.push(0); - } - } - - quickcheck! { - fn double_negation(x: UCN) -> bool { - let mut x2 = x.clone().not(); - expand_to_match(&mut x2, &x); - let mut x3 = x2.not(); - expand_to_match(&mut x3, &x); - x3 == x - } - } - - quickcheck! { - fn or_associative(a: UCN, b: UCN, c: UCN) -> bool { - ((&a | &b) | &c) == (&a | (&b | &c)) - } - fn xor_associative(a: UCN, b: UCN, c: UCN) -> bool { - ((&a ^ &b) ^ &c) == (&a ^ (&b ^ &c)) - } - fn and_associative(a: UCN, b: UCN, c: UCN) -> bool { - ((&a & &b) & &c) == (&a & (&b & &c)) - } - fn add_associative(a: UCN, b: UCN, c: UCN) -> bool { - ((&a + &b) + &c) == (&a + (&b + &c)) - } - fn mul_associative(a: UCN, b: UCN, c: UCN) -> bool { - ((&a * &b) * &c) == (&a * (&b * &c)) - } - } - - quickcheck! { - fn or_commutative(a: UCN, b: UCN) -> bool { - (&a | &b) == (&b | &a) - } - fn xor_commutative(a: UCN, b: UCN) -> bool { - (&a ^ &b) == (&b ^ &a) - } - fn and_commutative(a: UCN, b: UCN) -> bool { - (&a & &b) == (&b & &a) - } - fn add_commutative(a: UCN, b: UCN) -> bool { - let ab = &a + &b; - let ba = &b + &a; - (ab == ba) - } - fn mul_commutative(a: UCN, b: UCN) -> bool { - let ab = &a * &b; - let ba = &b * &a; - (ab == ba) - } - } - - quickcheck! { - fn or_identity(a: UCN) -> bool { - (&a | &UCN{ contents: vec![] }) == a - } - fn xor_identity(a: UCN) -> bool { - (&a ^ &UCN{ contents: vec![] }) == a - } - fn and_identity(a: UCN) -> bool { - let mut contents = Vec::new(); - contents.resize(a.contents.len(), 0xFFFFFFFFFFFFFFFF); - let effs = UCN{ contents: contents }; - (&a & &effs) == a - } - fn shl_identity(a: UCN) -> bool { - (&a << 0) == a - } - fn shr_identity(a: UCN) -> bool { - (&a << 0) == a - } - fn add_identity(a: UCN) -> bool { - (&a + &UCN{ contents: vec![] }) == a - } - fn sub_identity(a: UCN) -> bool { - (&a - &UCN{ contents: vec![] }) == a - } - fn mul_identity(a: UCN) -> bool { - let one = UCN{ contents: vec![1] }; - (&a * &one) == a - } - fn div_identity(a: UCN) -> bool { - let one = UCN{ contents: vec![1] }; - (&a / &one) == a - } - } - - quickcheck! { - fn or_annihilator(a: UCN) -> bool { - let mut contents = Vec::new(); - contents.resize(a.contents.len(), 0xFFFFFFFFFFFFFFFF); - let effs = UCN{ contents: contents }; - (&a | &effs) == effs - } - fn and_annihilator(a: UCN) -> bool { - let zero = UCN{ contents: vec![] }; - (&a & &zero) == zero - } - fn shl_shr_annihilate(a: UCN, b: u8) -> bool { - let left = &a << b; - let right = &left >> b; - right == a - } - fn sub_annihilation(a: UCN) -> bool { - (&a - &a) == UCN{ contents: vec![] } - } - fn mul_annihilation(a: UCN) -> bool { - let zero = UCN{ contents: vec![] }; - (&a * &zero) == zero - } - } - - quickcheck! { - fn xor_inverse(a: UCN, b: UCN) -> bool { - ((&a ^ &b) ^ &b) == a - } - fn or_idempotent(a: UCN, b: UCN) -> bool { - (&a | &b) == ((&a | &b) | &b) - } - fn and_idempotent(a: UCN, b: UCN) -> bool { - (&a & &b) == ((&a & &b) & &b) - } - fn andor_absorbtion(a: UCN, b: UCN) -> bool { - (&a & (&a | &b)) == a - } - fn orand_absorbtion(a: UCN, b: UCN) -> bool { - (&a | (&a & &b)) == a - } - } - - quickcheck! { - fn mod_plus1_identity(a: UCN) -> bool { - let one = UCN{ contents: vec![1] }; - let ap1 = &a + &one; - (&a % ap1) == a - } - fn mod_min1_is_one(a: UCN) -> bool { - let one = UCN{ contents: vec![1] }; - let am1 = &a - &one; - (&a % am1) == one - } - #[should_panic] - fn div0_fails(a: UCN) -> bool { - (&a / &UCN{ contents: vec![] }) == a - } - fn euclid_is_alive(a: UCN, b: UCN) -> bool { - let zero = UCN{ contents: vec![] }; - if &b == &zero { - return true; - } - let q = &a / &b; - let r = &a % &b; - let res = (b * q) + r; - a == res - } - } - - fn gold_test(name: &str, f: F) - where - F: Fn(UCN,UCN) -> UCN - { - let mut file = File::open(name).unwrap(); - let mut contents = String::new(); - file.read_to_string(&mut contents).unwrap(); - let mut iter = contents.lines(); - - while let Some(xstr) = iter.next() { - let ystr = iter.next().unwrap(); - let zstr = iter.next().unwrap(); - - assert!(xstr.starts_with("x: ")); - assert!(ystr.starts_with("y: ")); - assert!(zstr.starts_with("z: ")); - let x = UCN::from_str(&xstr[3..]); - let y = UCN::from_str(&ystr[3..]); - let z = UCN::from_str(&zstr[3..]); - assert_eq!(f(x,y), z); - } - } - - #[test] - fn add_tests() { - gold_test("tests/add_tests.txt", |x,y| x + y); - } - - #[test] - fn sub_tests() { - gold_test("tests/sub_tests.txt", |x,y| x - y); - } - - #[test] - fn mul_tests() { - gold_test("tests/mul_tests.txt", |x,y| x * y); - } - - #[test] - fn div_tests() { - gold_test("tests/div_tests.txt", |x,y| x / y); - } - - #[test] - fn mod_tests() { - gold_test("tests/mod_tests.txt", |x,y| x % y); - } - - quickcheck! { - fn and_over_or_distribution(a: UCN, b: UCN, c: UCN) -> bool { - (&a & (&b | &c)) == ((&a & &b) | (&a & &c)) - } - fn and_over_xor_distribution(a: UCN, b: UCN, c: UCN) -> bool { - (&a & (&b ^ &c)) == ((&a & &b) ^ (&a & &c)) - } - fn or_over_and_distribution(a: UCN, b: UCN, c: UCN) -> bool { - (&a | (&b & &c)) == ((&a | &b) & (&a | &c)) - } - fn demorgans(a: UCN, b: UCN) -> bool { - let mut a2 = if a.contents.len() < b.contents.len() {a.clone()} - else {b.clone()}; - let b2 = if a.contents.len() < b.contents.len() {b.clone()} - else {a.clone()}; - expand_to_match(&mut a2, &b2); - (!(&a2 | &b2)) == (!a2 & !b2) - } - fn shift_multiply_equiv(a: UCN, b: u8) -> bool { - let one = UCN{ contents: vec![1] }; - let pow2 = one << b; - (&a << b) == (&a * pow2) - } - } - -} +pub use self::signed::SCN; +pub use self::unsigned::UCN; diff --git a/src/cryptonum/signed.rs b/src/cryptonum/signed.rs new file mode 100644 index 0000000..4f05319 --- /dev/null +++ b/src/cryptonum/signed.rs @@ -0,0 +1,199 @@ +use cryptonum::unsigned::{UCN,divmod}; +use std::fmt; +use std::cmp::Ordering; +use std::fmt::Write; +use std::ops::*; + +/// In case you were wondering, it stands for "Signed Crypto Num". +#[derive(Clone,Debug,PartialEq,Eq)] +pub struct SCN { + negative: bool, + value: UCN +} + +impl SCN { + pub fn from_str(x: &str) -> SCN { + if x.get(0..1) == Some("-") { + SCN{ negative: true, value: UCN::from_str(&x[1..]) } + } else { + SCN{ negative: false, value: UCN::from_str(x) } + } + } +} + +impl fmt::UpperHex for SCN { + fn fmt(&self, fmt: &mut fmt::Formatter) -> Result<(),fmt::Error> { + if self.negative { + fmt.write_char('-')?; + } + self.value.fmt(fmt) + } +} + +//------------------------------------------------------------------------------ +// +// Conversions to/from crypto nums. +// +//------------------------------------------------------------------------------ + +define_signed_from!(SCN, i8, u8); +define_signed_from!(SCN, i16, u16); +define_signed_from!(SCN, i32, u32); +define_signed_from!(SCN, i64, u64); +define_signed_into!(SCN, i8, u8); +define_signed_into!(SCN, i16, u16); +define_signed_into!(SCN, i32, u32); +define_signed_into!(SCN, i64, u64); + +//------------------------------------------------------------------------------ +// +// Comparisons +// +//------------------------------------------------------------------------------ + +impl PartialOrd for SCN { + fn partial_cmp(&self, other: &SCN) -> Option { + Some(self.cmp(other)) + } +} + +impl Ord for SCN { + fn cmp(&self, other: &SCN) -> Ordering { + match (self.negative, other.negative) { + (false, false) => self.value.cmp(&other.value), + (false, true) => Ordering::Greater, + (true, false) => Ordering::Less, + (true, true) => self.value.cmp(&other.value).reverse() + } + } +} + +//------------------------------------------------------------------------------ +// +// Arithmetic +// +//------------------------------------------------------------------------------ + +impl<'a> AddAssign<&'a SCN> for SCN { + fn add_assign(&mut self, rhs: &SCN) { + if self.negative == rhs.negative { + self.value.add_assign(&rhs.value); + } else { + if self.value >= rhs.value { + self.value.sub_assign(&rhs.value); + } else { + self.negative = !self.negative; + self.value = &rhs.value - &self.value; + } + } + } +} + +impl<'a> SubAssign<&'a SCN> for SCN { + fn sub_assign(&mut self, rhs: &SCN) { + let flipped = SCN{ negative: !rhs.negative, value: rhs.value.clone() }; + self.add_assign(&flipped); + } +} + +impl<'a> MulAssign<&'a SCN> for SCN { + fn mul_assign(&mut self, rhs: &SCN) { + self.negative ^= rhs.negative; + self.value.mul_assign(&rhs.value); + } +} + +impl<'a> DivAssign<&'a SCN> for SCN { + fn div_assign(&mut self, rhs: &SCN) { + self.negative ^= rhs.negative; + // rounding makes me grumpy + let mut remainder = Vec::new(); + let copy = self.value.contents.clone(); + divmod(&mut self.value.contents, &mut remainder, + ©, &rhs.value.contents); + if self.negative { + let one = UCN{ contents: vec![1] }; + self.sub_assign(SCN{ negative: false, value: one}); + } + } +} + +impl<'a> RemAssign<&'a SCN> for SCN { + fn rem_assign(&mut self, rhs: &SCN) { + let base = &self.value % &rhs.value; + + if self.negative == rhs.negative { + self.value = base; + } else { + self.negative = rhs.negative; + self.value = &rhs.value - &base; + } + } +} + +derive_arithmetic_operators!(SCN, Add, add, AddAssign, add_assign); +derive_arithmetic_operators!(SCN, Sub, sub, SubAssign, sub_assign); +derive_arithmetic_operators!(SCN, Mul, mul, MulAssign, mul_assign); +derive_arithmetic_operators!(SCN, Div, div, DivAssign, div_assign); +derive_arithmetic_operators!(SCN, Rem, rem, RemAssign, rem_assign); + +//------------------------------------------------------------------------------ +// +// Tests! +// +//------------------------------------------------------------------------------ + +#[cfg(test)] +mod test { + use std::fs::File; + use std::io::Read; + use super::*; + + fn gold_test(name: &str, f: F) + where + F: Fn(SCN,SCN) -> SCN + { + let mut file = File::open(name).unwrap(); + let mut contents = String::new(); + file.read_to_string(&mut contents).unwrap(); + let mut iter = contents.lines(); + + while let Some(xstr) = iter.next() { + let ystr = iter.next().unwrap(); + let zstr = iter.next().unwrap(); + + assert!(xstr.starts_with("x: ")); + assert!(ystr.starts_with("y: ")); + assert!(zstr.starts_with("z: ")); + let x = SCN::from_str(&xstr[3..]); + let y = SCN::from_str(&ystr[3..]); + let z = SCN::from_str(&zstr[3..]); + assert_eq!(f(x,y), z); + } + } + + #[test] + fn add_tests() { + gold_test("tests/add_tests_signed.txt", |x,y| x + y); + } + + #[test] + fn sub_tests() { + gold_test("tests/sub_tests_signed.txt", |x,y| x - y); + } + + #[test] + fn mul_tests() { + gold_test("tests/mul_tests_signed.txt", |x,y| x * y); + } + + #[test] + fn div_tests() { + gold_test("tests/div_tests_signed.txt", |x,y| x / y); + } + + #[test] + fn mod_tests() { + gold_test("tests/mod_tests_signed.txt", |x,y| x % y); + } +} diff --git a/src/cryptonum/unsigned.rs b/src/cryptonum/unsigned.rs new file mode 100644 index 0000000..6e44f12 --- /dev/null +++ b/src/cryptonum/unsigned.rs @@ -0,0 +1,1046 @@ +use num::{BigUint,ToPrimitive,Zero}; +use std::fmt; +use std::fmt::Write; +use std::cmp::Ordering; +use std::ops::*; + +/// In case you were wondering, it stands for "Unsigned Crypto Num". +#[derive(Clone,Debug,PartialEq,Eq)] +pub struct UCN { + pub(crate) contents: Vec +} + +impl UCN { + fn clean(&mut self) { + loop { + match self.contents.pop() { + None => + break, + Some(0) => + continue, + Some(x) => { + self.contents.push(x); + break + } + } + } + } + + fn expand(&mut self, rhs: &UCN) { + while self.contents.len() < rhs.contents.len() { + self.contents.push(0); + } + } + + pub fn from_str(x: &str) -> UCN { + let mut outvec = Vec::new(); + let mut worker = 0; + let mut shift = 0; + + for c in x.chars().rev() { + match c.to_digit(16) { + None => + panic!("Bad character in string: {}", c), + Some(v) => { + worker = worker + ((v as u64) << shift); + shift += 4; + } + } + if shift == 64 { + outvec.push(worker); + worker = 0; + shift = 0; + } + } + outvec.push(worker); + let mut res = UCN{ contents: outvec }; + res.clean(); + res + } +} + +impl fmt::UpperHex for UCN { + fn fmt(&self, fmt: &mut fmt::Formatter) -> Result<(),fmt::Error> { + for x in self.contents.iter().rev() { + fmt.write_char(tochar_upper(x >> 60))?; + fmt.write_char(tochar_upper(x >> 56))?; + fmt.write_char(tochar_upper(x >> 52))?; + fmt.write_char(tochar_upper(x >> 48))?; + fmt.write_char(tochar_upper(x >> 44))?; + fmt.write_char(tochar_upper(x >> 40))?; + fmt.write_char(tochar_upper(x >> 36))?; + fmt.write_char(tochar_upper(x >> 32))?; + fmt.write_char(tochar_upper(x >> 28))?; + fmt.write_char(tochar_upper(x >> 24))?; + fmt.write_char(tochar_upper(x >> 20))?; + fmt.write_char(tochar_upper(x >> 16))?; + fmt.write_char(tochar_upper(x >> 12))?; + fmt.write_char(tochar_upper(x >> 8))?; + fmt.write_char(tochar_upper(x >> 4))?; + fmt.write_char(tochar_upper(x >> 0))?; + } + Ok(()) + } +} + +fn tochar_upper(x: u64) -> char { + match (x as u8) & (0xF as u8) { + 0x0 => '0', + 0x1 => '1', + 0x2 => '2', + 0x3 => '3', + 0x4 => '4', + 0x5 => '5', + 0x6 => '6', + 0x7 => '7', + 0x8 => '8', + 0x9 => '9', + 0xA => 'A', + 0xB => 'B', + 0xC => 'C', + 0xD => 'D', + 0xE => 'E', + 0xF => 'F', + _ => panic!("the world is broken") + } +} + +impl fmt::LowerHex for UCN { + fn fmt(&self, fmt: &mut fmt::Formatter) -> Result<(),fmt::Error> { + for x in self.contents.iter().rev() { + fmt.write_char(tochar_lower(x >> 60))?; + fmt.write_char(tochar_lower(x >> 56))?; + fmt.write_char(tochar_lower(x >> 52))?; + fmt.write_char(tochar_lower(x >> 48))?; + fmt.write_char(tochar_lower(x >> 44))?; + fmt.write_char(tochar_lower(x >> 40))?; + fmt.write_char(tochar_lower(x >> 36))?; + fmt.write_char(tochar_lower(x >> 32))?; + fmt.write_char(tochar_lower(x >> 28))?; + fmt.write_char(tochar_lower(x >> 24))?; + fmt.write_char(tochar_lower(x >> 20))?; + fmt.write_char(tochar_lower(x >> 16))?; + fmt.write_char(tochar_lower(x >> 12))?; + fmt.write_char(tochar_lower(x >> 8))?; + fmt.write_char(tochar_lower(x >> 4))?; + fmt.write_char(tochar_lower(x >> 0))?; + } + Ok(()) + } +} + +fn tochar_lower(x: u64) -> char { + match (x as u8) & (0xF as u8) { + 0x0 => '0', + 0x1 => '1', + 0x2 => '2', + 0x3 => '3', + 0x4 => '4', + 0x5 => '5', + 0x6 => '6', + 0x7 => '7', + 0x8 => '8', + 0x9 => '9', + 0xA => 'a', + 0xB => 'b', + 0xC => 'c', + 0xD => 'd', + 0xE => 'e', + 0xF => 'f', + _ => panic!("the world is broken") + } +} + +//------------------------------------------------------------------------------ +// +// Conversions to/from crypto nums. +// +//------------------------------------------------------------------------------ + +define_from!(UCN, u8); +define_from!(UCN, u16); +define_from!(UCN, u32); +define_from!(UCN, u64); +define_into!(UCN, u8); +define_into!(UCN, u16); +define_into!(UCN, u32); +define_into!(UCN, u64); + +impl From for UCN { + fn from(mut x: BigUint) -> UCN { + let mut dest = Vec::new(); + let mask = BigUint::from(0xFFFFFFFFFFFFFFFF as u64); + + while !x.is_zero() { + match (&x & &mask).to_u64() { + None => + panic!("Can't use BigUint in From"), + Some(val) => + dest.push(val) + } + x >>= 64; + } + + UCN{ contents: dest } + } +} + +impl Into for UCN { + fn into(self) -> BigUint { + let mut result = BigUint::zero(); + + for part in self.contents.iter().rev() { + result <<= 64; + result += BigUint::from(*part); + } + + result + } +} + +//------------------------------------------------------------------------------ +// +// Comparisons +// +//------------------------------------------------------------------------------ + +impl PartialOrd for UCN { + fn partial_cmp(&self, other: &UCN) -> Option { + Some(self.cmp(other)) + } +} + +impl Ord for UCN { + fn cmp(&self, other: &UCN) -> Ordering { + match self.contents.len().cmp(&other.contents.len()) { + Ordering::Equal => { + let mut me = self.contents.iter().rev(); + let mut them = other.contents.iter().rev(); + + for (m, t) in me.zip(them) { + match m.cmp(t) { + Ordering::Equal => + continue, + res => + return res + } + } + + Ordering::Equal + } + x => x + } + } +} + +//------------------------------------------------------------------------------ +// +// Bit Operations +// +//------------------------------------------------------------------------------ + +impl Not for UCN { + type Output = UCN; + + fn not(self) -> UCN { + let mut contents = self.contents; + + for x in contents.iter_mut() { + *x = !*x; + } + + let mut res = UCN{ contents: contents }; + res.clean(); + res + } +} + +impl<'a> Not for &'a UCN { + type Output = UCN; + + fn not(self) -> UCN { + let res = self.clone(); + res.not() + } +} + +impl<'a> BitOrAssign<&'a UCN> for UCN { + fn bitor_assign(&mut self, rhs: &UCN) { + self.expand(&rhs); + { + let mut iter_me = self.contents.iter_mut(); + let mut iter_tm = rhs.contents.iter(); + + loop { + match (iter_me.next(), iter_tm.next()) { + (Some(dest), Some(val)) => + *dest |= val, + _ => + break + } + } + } + self.clean(); + } +} + +impl<'a> BitXorAssign<&'a UCN> for UCN { + fn bitxor_assign(&mut self, rhs: &UCN) { + self.expand(&rhs); + { + let mut iter_me = self.contents.iter_mut(); + let mut iter_tm = rhs.contents.iter(); + + loop { + match (iter_me.next(), iter_tm.next()) { + (Some(dest), Some(val)) => + *dest ^= val, + _ => + break + } + } + } + self.clean(); + } +} + +impl<'a> BitAndAssign<&'a UCN> for UCN { + fn bitand_assign(&mut self, rhs: &UCN) { + if self.contents.len() > rhs.contents.len() { + self.contents.resize(rhs.contents.len(), 0); + } + { + let mut iter_me = self.contents.iter_mut(); + let mut iter_tm = rhs.contents.iter(); + + loop { + match (iter_me.next(), iter_tm.next()) { + (Some(dest), Some(val)) => + *dest &= val, + _ => + break + } + } + } + self.clean(); + } +} + +derive_arithmetic_operators!(UCN, BitOr, bitor, BitOrAssign, bitor_assign); +derive_arithmetic_operators!(UCN, BitXor, bitxor, BitXorAssign, bitxor_assign); +derive_arithmetic_operators!(UCN, BitAnd, bitand, BitAndAssign, bitand_assign); + +//------------------------------------------------------------------------------ +// +// Shifts +// +//------------------------------------------------------------------------------ + +impl ShlAssign for UCN { + fn shl_assign(&mut self, rhs: u64) { + let mut digits = rhs / 64; + let bits = rhs % 64; + let mut carry = 0; + + // ripple the bit-level shift through + if bits != 0 { + for x in self.contents.iter_mut() { + let new_carry = *x >> (64 - bits); + *x = (*x << bits) | carry; + carry = new_carry; + } + } + + // if we pulled some stuff off the end, add it back + if carry != 0 { + self.contents.push(carry); + } + + // add the appropriate digits on the low side + while digits > 0 { + self.contents.insert(0,0); + digits -= 1; + } + } +} + +impl Shl for UCN { + type Output = UCN; + + fn shl(self, rhs: u64) -> UCN { + let mut copy = self.clone(); + copy.shl_assign(rhs); + copy + } +} + +derive_shift_operators!(UCN, ShlAssign, Shl, shl_assign, shl, usize); +derive_shift_operators!(UCN, ShlAssign, Shl, shl_assign, shl, u32); +derive_shift_operators!(UCN, ShlAssign, Shl, shl_assign, shl, u16); +derive_shift_operators!(UCN, ShlAssign, Shl, shl_assign, shl, u8); + +impl ShrAssign for UCN { + fn shr_assign(&mut self, rhs: u64) { + let mut digits = rhs / 64; + let bits = rhs % 64; + + // remove the appropriate digits on the low side + while digits > 0 { + self.contents.remove(0); + digits -= 1; + } + // ripple the shifts over + let mut carry = 0; + let mask = !(0xFFFFFFFFFFFFFFFF << bits); + + for x in self.contents.iter_mut().rev() { + let base = *x >> bits; + let (new_carry, _) = (*x & mask).overflowing_shl((64-bits) as u32); + *x = base | carry; + carry = new_carry; + } + // in this case, we just junk the extra carry bits, but we do need to + // cleanup possible zeros at the end. + self.clean(); + } +} + +impl Shr for UCN { + type Output = UCN; + + fn shr(self, rhs: u64) -> UCN { + let mut copy = self.clone(); + copy.shr_assign(rhs); + copy + } +} + +derive_shift_operators!(UCN, ShrAssign, Shr, shr_assign, shr, usize); +derive_shift_operators!(UCN, ShrAssign, Shr, shr_assign, shr, u32); +derive_shift_operators!(UCN, ShrAssign, Shr, shr_assign, shr, u16); +derive_shift_operators!(UCN, ShrAssign, Shr, shr_assign, shr, u8); + +derive_signed_shift_operators!(UCN, usize, isize); +derive_signed_shift_operators!(UCN, u64, i64); +derive_signed_shift_operators!(UCN, u32, i32); +derive_signed_shift_operators!(UCN, u16, i16); +derive_signed_shift_operators!(UCN, u8, i8); + +//------------------------------------------------------------------------------ +// +// Addition, Subtraction and Multiplication +// +//------------------------------------------------------------------------------ + +impl<'a> AddAssign<&'a UCN> for UCN { + fn add_assign(&mut self, rhs: &UCN) { + let mut iter_tm = rhs.contents.iter(); + let mut stolen = None; + let mut carry = 0; + + // loop through every element on the left hand side, breaking early + // on if we right the end of the left hand side. + { + let mut iter_me = self.contents.iter_mut(); + loop { + match(iter_me.next(), iter_tm.next()) { + (None, None) => + break, + (Some(dest), None) => { + let dest128 = *dest as u128; + let newdest = dest128 + carry; + *dest = newdest as u64; + carry = newdest >> 64; + } + (None, Some(x)) => { + stolen = Some(*x); + break; + } + (Some(dest), Some(r)) => { + let newdest = (*dest as u128) + (*r as u128) + carry; + *dest = newdest as u64; + carry = newdest >> 64; + } + } + } + } + // if we accidentally stole something form the right iterator, + // push it back on. + if let Some(x) = stolen { + let stolen128 = (x as u128) + carry; + self.contents.push(stolen128 as u64); + carry = stolen128 >> 64; + } + // now loop through any remaining items on the right hand side, + // pushing them onto the result. + for x in iter_tm { + let x128 = (*x as u128) + carry; + self.contents.push(x128 as u64); + carry = x128 >> 64; + } + // finally, if there's still a carry, push it on the end. + if carry > 0 { + self.contents.push(carry as u64); + } + } +} + +impl<'a> SubAssign<&'a UCN> for UCN { + fn sub_assign(&mut self, rhs: &UCN) { + { + let mut borrow = 0; + let mut iter_me = self.contents.iter_mut(); + let mut iter_tm = rhs.contents.iter(); + + loop { + assert!( (borrow == 0) | (borrow == 1) ); + match (iter_me.next(), iter_tm.next()) { + (None, None) if borrow == 0 => + break, + (None, None) => + panic!("Generated negative UCN in subtraction (1)."), + (Some(x), None) => { + if borrow == 0 { + break; + } + if *x == 0 { + *x = 0xFFFFFFFFFFFFFFFF; + borrow = 1; + } else { + *x = *x - borrow; + break; + } + } + (None, Some(_)) => { + panic!("Generated negative UCN in subtraction (2)."); + } + (Some(x), Some(y)) => { + if (*x - borrow) >= *y { + *x = (*x - borrow) - *y; + borrow = 0; + } else { + let x128 = (*x as u128) + 0x10000000000000000; + let res = x128 - (*y as u128) - (borrow as u128); + *x = res as u64; + borrow = 1; + } + } + } + } + } + self.clean(); + } +} + +impl<'a> MulAssign<&'a UCN> for UCN { + fn mul_assign(&mut self, rhs: &UCN) { + // Handle the quick and easy multiplication by zero cases first. + if self.contents.len() == 0 { + return; + } + if rhs.contents.len() == 0 { + self.contents.resize(0,0); + return; + } + + // OK, do some real multiplication + let x = self.contents.clone(); + let y = rhs.contents.clone(); + let outlen = x.len() + y.len(); + let n = y.len() - 1; + + // this algorithm is 14.12 from "Handbook of Applied Cryptography" + self.contents.resize(0, 0); + self.contents.resize(outlen, 0); + for (i,xi) in x.iter().enumerate() { + let mut c = 0; + for (j,yj) in y.iter().enumerate() { + let wij = self.contents[i+j] as u128; + let xjyi = (*xi as u128) * (*yj as u128); + let uv = wij + xjyi + c; + self.contents[i+j] = uv as u64; + c = uv >> 64; + } + self.contents[i+n+1] = c as u64; + } + self.clean(); + } +} + +pub fn divmod(quotient: &mut Vec, remainder: &mut Vec, + inx: &Vec, iny: &Vec) +{ + quotient.resize(0,0); + remainder.resize(0,0); + // This algorithm is 14.20 from "Handbook of Applied Cryptography" + // + // It requires that y[t] is not zero, which it isn't due to our invariant + // that we don't have unnecessary zeros at the end of the array. We note + // that it's also very convienent if the top bit of y[t] is set, as well, + // so we shift everything left so that things work out. + let mut xbuffer = Vec::with_capacity(inx.len() + 2); + let mut ybuffer = Vec::with_capacity(iny.len() + 2); + xbuffer.extend_from_slice(&inx); + ybuffer.extend_from_slice(&iny); + let mut x = UCN{ contents: xbuffer }; + let mut y = UCN{ contents: ybuffer }; + let additional_shift = iny[iny.len() - 1].leading_zeros() as usize; + x <<= additional_shift; + y <<= additional_shift; + // Once we've done this, we should be good to go with our mostly-correct + // x and y. The only trick is that the algorithm requires that n >= t. If + // this is not true, then the answer is zero, because the divisor is greater + // than the dividend. + let n = x.contents.len(); + let t = y.contents.len(); + if n < t { + remainder.extend_from_slice(&inx); + return; + } + // Also, it's real convient for n and t to be greater than one, which we + // achieve by pushing a zero into the low digit. Because we do this, we + // don't have to do a lot of testing against negative indices later. + x.contents.insert(0,0); + y.contents.insert(0,0); + // 1. For j from 0 to (n-t) do: qj <- 0. + let mut q = Vec::with_capacity(n - t + 1); + q.resize(n - t + 1, 0); + // 2. While (x >= yb^(n-t)) do the following: + // q_(n-t) <- q_(n-t) + 1 + // x <- x - yb^(n-t) + let ybnt = &y << (64 * (n - t)); + while &x >= &ybnt { + q[n-t] = q[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 xi = yt, then set q_(i-t-1) <- b - 1; otherwise set + // q_(i-t-1) <- floor((x_i * b + x_(i-1)) /y_t). + if x.contents[i] == y.contents[t] { + q[i-t-1] = 0xFFFFFFFFFFFFFFFF; + } else { + let top = ((x.contents[i] as u128)<<64) + (x.contents[i-1] as u128); + let bot = y.contents[t] as u128; + let solution = top / bot; + q[i-t-1] = solution as u64; + } + // 3.2. While (q_(i-t-1)(y_t * b + y_(t-1)) > x_i(b2) + x_(i-1)b + + // x_(i-2)) do: + // q_(i - t - 1) <- q_(i - t 1) - 1. + loop { + let qit1 = UCN{ contents: vec![q[i - t - 1]] }; + let ytbyt1 = UCN{ contents: vec![y.contents[t-1], y.contents[t]] }; + let left = qit1 * ytbyt1; + let right = UCN{ contents: vec![x.contents[i-2], + x.contents[i-1], + x.contents[i]] }; + + if left <= right { + break + } + + q[i - t - 1] -= 1; + } + // 3.3. x <- x - q_(i - t - 1) * y * b^(i-t-1) + let qit1 = UCN{ contents: vec![q[i - t - 1]] }; + let ybit1 = &y << (64 * (i - t - 1)); + let subbit = &qit1 * &ybit1; + if subbit <= x { + x -= subbit; + } else { + // 3.4. if x < 0 then set z <- x + yb^(i-t-1) and + // q_(i-t-1) <- q(i-t-1) - 1 + x -= subbit - ybit1; + q[i - t - 1] -= 1; + } + i -= 1; + } + // 4. r <- x + x >>= additional_shift; + if x.contents.len() > 0 { + // remember, we added a zero to the front of + // everything earlier; this removes it. + x.contents.remove(0); + } + remainder.append(&mut x.contents); + // 5. return (q,r) + while (q.len() > 0) && (q[q.len() - 1] == 0) { + q.pop(); + } + quotient.append(&mut q); +} + +impl<'a> DivAssign<&'a UCN> for UCN { + fn div_assign(&mut self, rhs: &UCN) { + let copy = self.contents.clone(); + let mut dead = Vec::new(); + divmod(&mut self.contents, &mut dead, ©, &rhs.contents); + } +} + +impl<'a> RemAssign<&'a UCN> for UCN { + fn rem_assign(&mut self, rhs: &UCN) { + let copy = self.contents.clone(); + let mut dead = Vec::new(); + divmod(&mut dead, &mut self.contents, ©, &rhs.contents); + } +} + +derive_arithmetic_operators!(UCN, Add, add, AddAssign, add_assign); +derive_arithmetic_operators!(UCN, Sub, sub, SubAssign, sub_assign); +derive_arithmetic_operators!(UCN, Mul, mul, MulAssign, mul_assign); +derive_arithmetic_operators!(UCN, Div, div, DivAssign, div_assign); +derive_arithmetic_operators!(UCN, Rem, rem, RemAssign, rem_assign); + +//------------------------------------------------------------------------------ +// +// Tests! +// +//------------------------------------------------------------------------------ + +#[cfg(test)] +mod test { + use quickcheck::{Arbitrary,Gen}; + use std::fs::File; + use std::io::Read; + use super::*; + + #[test] + fn test_clean() { + let mut val1 = UCN{ contents: vec![1,0,0] }; + val1.clean(); + assert_eq!(val1, UCN{ contents: vec![1] }); + // + let mut val2 = UCN{ contents: vec![0,0,0] }; + val2.clean(); + assert_eq!(val2, UCN{ contents: vec![] }); + // + let mut val3 = UCN{ contents: vec![1,0,1] }; + val3.clean(); + assert_eq!(val3, UCN{ contents: vec![1,0,1] }); + // + let mut val4 = UCN{ contents: vec![] }; + val4.clean(); + assert_eq!(val4, UCN{ contents: vec![] }); + } + + #[test] + #[allow(overflowing_literals)] + fn test_builders() { + assert_eq!(UCN{ contents: vec![] }, + UCN::from(0 as u8)); + assert_eq!(UCN{ contents: vec![0x7F] }, + UCN::from(0x7F as u8)); + assert_eq!(UCN{ contents: vec![0x7F7F] }, + UCN::from(0x7F7F as u16)); + assert_eq!(UCN{ contents: vec![0xCA5CADE5] }, + UCN::from(0xCA5CADE5 as u32)); + assert_eq!(UCN{ contents: vec![0xFFFFFFFFFFFFFFFF] }, + UCN::from(0xFFFFFFFFFFFFFFFF as u64)); + assert_eq!(UCN{ contents: vec![0x00000000FFFFFFFF] }, + UCN::from(0xFFFFFFFFFFFFFFFF as u32)); + } + + quickcheck! { + fn builder_u8_upgrade_u16(x: u8) -> bool { + UCN::from(x) == UCN::from(x as u16) + } + fn builder_u16_upgrade_u32(x: u16) -> bool { + UCN::from(x) == UCN::from(x as u32) + } + fn builder_u32_upgrade_u64(x: u32) -> bool { + UCN::from(x) == UCN::from(x as u64) + } + fn builder_u8_roundtrips(x: u8) -> bool { + let thereback: u8 = UCN::from(x).into(); + x == thereback + } + fn builder_u16_roundtrips(x: u16) -> bool { + let thereback: u16 = UCN::from(x).into(); + x == thereback + } + fn builder_u32_roundtrips(x: u32) -> bool { + let thereback: u32 = UCN::from(x).into(); + x == thereback + } + fn builder_u64_roundtrips(x: u64) -> bool { + let thereback: u64 = UCN::from(x).into(); + x == thereback + } + } + + quickcheck! { + fn u64_comparison_sane(x: u64, y: u64) -> bool { + let ucnx = UCN::from(x); + let ucny = UCN::from(y); + ucnx.cmp(&ucny) == x.cmp(&y) + } + fn longer_is_greater(x: u64, y: u64) -> bool { + if x == 0 { + true + } else { + let ucnx = UCN{ contents: vec![x, 1] }; + let ucny = UCN::from(y); + ucnx.cmp(&ucny) == Ordering::Greater + } + } + fn self_is_equal(x: Vec) -> bool { + let val = UCN{ contents: x }; + let copy = val.clone(); + + (&val == ©) && (val.cmp(©) == Ordering::Equal) + } + } + + impl Arbitrary for UCN { + fn arbitrary(g: &mut G) -> UCN { + let lenopts = [4,8,16,32,48,64,112,128,240]; + let mut len = *g.choose(&lenopts).unwrap(); + let mut contents = Vec::with_capacity(len); + + while len > 0 { + contents.push(g.gen()); + len -= 1; + } + UCN{ contents: contents } + } + } + + fn expand_to_match(a: &mut UCN, b: &UCN) { + assert!(a.contents.len() <= b.contents.len()); + while a.contents.len() < b.contents.len() { + a.contents.push(0); + } + } + + quickcheck! { + fn double_negation(x: UCN) -> bool { + let mut x2 = x.clone().not(); + expand_to_match(&mut x2, &x); + let mut x3 = x2.not(); + expand_to_match(&mut x3, &x); + x3 == x + } + } + + quickcheck! { + fn or_associative(a: UCN, b: UCN, c: UCN) -> bool { + ((&a | &b) | &c) == (&a | (&b | &c)) + } + fn xor_associative(a: UCN, b: UCN, c: UCN) -> bool { + ((&a ^ &b) ^ &c) == (&a ^ (&b ^ &c)) + } + fn and_associative(a: UCN, b: UCN, c: UCN) -> bool { + ((&a & &b) & &c) == (&a & (&b & &c)) + } + fn add_associative(a: UCN, b: UCN, c: UCN) -> bool { + ((&a + &b) + &c) == (&a + (&b + &c)) + } + fn mul_associative(a: UCN, b: UCN, c: UCN) -> bool { + ((&a * &b) * &c) == (&a * (&b * &c)) + } + } + + quickcheck! { + fn or_commutative(a: UCN, b: UCN) -> bool { + (&a | &b) == (&b | &a) + } + fn xor_commutative(a: UCN, b: UCN) -> bool { + (&a ^ &b) == (&b ^ &a) + } + fn and_commutative(a: UCN, b: UCN) -> bool { + (&a & &b) == (&b & &a) + } + fn add_commutative(a: UCN, b: UCN) -> bool { + let ab = &a + &b; + let ba = &b + &a; + (ab == ba) + } + fn mul_commutative(a: UCN, b: UCN) -> bool { + let ab = &a * &b; + let ba = &b * &a; + (ab == ba) + } + } + + quickcheck! { + fn or_identity(a: UCN) -> bool { + (&a | &UCN{ contents: vec![] }) == a + } + fn xor_identity(a: UCN) -> bool { + (&a ^ &UCN{ contents: vec![] }) == a + } + fn and_identity(a: UCN) -> bool { + let mut contents = Vec::new(); + contents.resize(a.contents.len(), 0xFFFFFFFFFFFFFFFF); + let effs = UCN{ contents: contents }; + (&a & &effs) == a + } + fn shl_identity(a: UCN) -> bool { + (&a << 0) == a + } + fn shr_identity(a: UCN) -> bool { + (&a << 0) == a + } + fn add_identity(a: UCN) -> bool { + (&a + &UCN{ contents: vec![] }) == a + } + fn sub_identity(a: UCN) -> bool { + (&a - &UCN{ contents: vec![] }) == a + } + fn mul_identity(a: UCN) -> bool { + let one = UCN{ contents: vec![1] }; + (&a * &one) == a + } + fn div_identity(a: UCN) -> bool { + let one = UCN{ contents: vec![1] }; + (&a / &one) == a + } + } + + quickcheck! { + fn or_annihilator(a: UCN) -> bool { + let mut contents = Vec::new(); + contents.resize(a.contents.len(), 0xFFFFFFFFFFFFFFFF); + let effs = UCN{ contents: contents }; + (&a | &effs) == effs + } + fn and_annihilator(a: UCN) -> bool { + let zero = UCN{ contents: vec![] }; + (&a & &zero) == zero + } + fn shl_shr_annihilate(a: UCN, b: u8) -> bool { + let left = &a << b; + let right = &left >> b; + right == a + } + fn sub_annihilation(a: UCN) -> bool { + (&a - &a) == UCN{ contents: vec![] } + } + fn mul_annihilation(a: UCN) -> bool { + let zero = UCN{ contents: vec![] }; + (&a * &zero) == zero + } + } + + quickcheck! { + fn xor_inverse(a: UCN, b: UCN) -> bool { + ((&a ^ &b) ^ &b) == a + } + fn or_idempotent(a: UCN, b: UCN) -> bool { + (&a | &b) == ((&a | &b) | &b) + } + fn and_idempotent(a: UCN, b: UCN) -> bool { + (&a & &b) == ((&a & &b) & &b) + } + fn andor_absorbtion(a: UCN, b: UCN) -> bool { + (&a & (&a | &b)) == a + } + fn orand_absorbtion(a: UCN, b: UCN) -> bool { + (&a | (&a & &b)) == a + } + } + + quickcheck! { + fn mod_plus1_identity(a: UCN) -> bool { + let one = UCN{ contents: vec![1] }; + let ap1 = &a + &one; + (&a % ap1) == a + } + fn mod_min1_is_one(a: UCN) -> bool { + let one = UCN{ contents: vec![1] }; + let am1 = &a - &one; + (&a % am1) == one + } + #[should_panic] + fn div0_fails(a: UCN) -> bool { + (&a / &UCN{ contents: vec![] }) == a + } + fn euclid_is_alive(a: UCN, b: UCN) -> bool { + let zero = UCN{ contents: vec![] }; + if &b == &zero { + return true; + } + let q = &a / &b; + let r = &a % &b; + let res = (b * q) + r; + a == res + } + } + + fn gold_test(name: &str, f: F) + where + F: Fn(UCN,UCN) -> UCN + { + let mut file = File::open(name).unwrap(); + let mut contents = String::new(); + file.read_to_string(&mut contents).unwrap(); + let mut iter = contents.lines(); + + while let Some(xstr) = iter.next() { + let ystr = iter.next().unwrap(); + let zstr = iter.next().unwrap(); + + assert!(xstr.starts_with("x: ")); + assert!(ystr.starts_with("y: ")); + assert!(zstr.starts_with("z: ")); + let x = UCN::from_str(&xstr[3..]); + let y = UCN::from_str(&ystr[3..]); + let z = UCN::from_str(&zstr[3..]); + assert_eq!(f(x,y), z); + } + } + + #[test] + fn add_tests() { + gold_test("tests/add_tests.txt", |x,y| x + y); + } + + #[test] + fn sub_tests() { + gold_test("tests/sub_tests.txt", |x,y| x - y); + } + + #[test] + fn mul_tests() { + gold_test("tests/mul_tests.txt", |x,y| x * y); + } + + #[test] + fn div_tests() { + gold_test("tests/div_tests.txt", |x,y| x / y); + } + + #[test] + fn mod_tests() { + gold_test("tests/mod_tests.txt", |x,y| x % y); + } + + quickcheck! { + fn and_over_or_distribution(a: UCN, b: UCN, c: UCN) -> bool { + (&a & (&b | &c)) == ((&a & &b) | (&a & &c)) + } + fn and_over_xor_distribution(a: UCN, b: UCN, c: UCN) -> bool { + (&a & (&b ^ &c)) == ((&a & &b) ^ (&a & &c)) + } + fn or_over_and_distribution(a: UCN, b: UCN, c: UCN) -> bool { + (&a | (&b & &c)) == ((&a | &b) & (&a | &c)) + } + fn demorgans(a: UCN, b: UCN) -> bool { + let mut a2 = if a.contents.len() < b.contents.len() {a.clone()} + else {b.clone()}; + let b2 = if a.contents.len() < b.contents.len() {b.clone()} + else {a.clone()}; + expand_to_match(&mut a2, &b2); + (!(&a2 | &b2)) == (!a2 & !b2) + } + fn shift_multiply_equiv(a: UCN, b: u8) -> bool { + let one = UCN{ contents: vec![1] }; + let pow2 = one << b; + (&a << b) == (&a * pow2) + } + } + +} diff --git a/src/lib.rs b/src/lib.rs index b048471..385e7c6 100644 --- a/src/lib.rs +++ b/src/lib.rs @@ -22,9 +22,4 @@ pub mod cryptonum; #[cfg(test)] mod test { - - #[test] - fn testing_works() { - assert!(true); - } } diff --git a/tests/add_tests_signed.txt b/tests/add_tests_signed.txt new file mode 100644 index 0000000..b217be7 --- /dev/null +++ b/tests/add_tests_signed.txt @@ -0,0 +1,6003 @@ +x: 6d31f0afbf39952568e869f6d4f55665980610d9cd35e2372c3a532a5cd0b7cf03721ed0b3ebf53c9326c9ce80e19202 +y: 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