diff --git a/src/uint.rs b/src/uint.rs index 5073747eb..2ae2bc44f 100644 --- a/src/uint.rs +++ b/src/uint.rs @@ -35,13 +35,30 @@ macro_rules! impl_map_from { } } +macro_rules! overflowing { + ($op: expr, $overflow: expr) => ( + { + let (overflow_x, overflow_overflow) = $op; + $overflow |= overflow_overflow; + overflow_x + } + ); + ($op: expr) => ( + { + let (overflow_x, _overflow_overflow) = $op; + overflow_x + } + ); +} + macro_rules! panic_on_overflow { - ($name:expr) => { + ($name: expr) => { if $name { panic!("arithmetic operation overflow") } } } + pub trait Uint: Sized + Default + FromStr + From + FromJson + fmt::Debug + fmt::Display + PartialOrd + Ord + PartialEq + Eq + Hash { /// Size of this type. @@ -67,11 +84,19 @@ pub trait Uint: Sized + Default + FromStr + From + FromJson + fmt::Debug + /// Return the least number of bits needed to represent the number fn bits(&self) -> usize; + /// Return if specific bit is set fn bit(&self, index: usize) -> bool; + /// Return single byte fn byte(&self, index: usize) -> u8; + /// Get this Uint as slice of bytes fn to_bytes(&self, bytes: &mut[u8]); + /// Create `Uint(10**n)` fn exp10(n: usize) -> Self; + /// Return eponentation `self**other`. Panic on overflow. + fn pow(self, other: Self) -> Self; + /// Return wrapped eponentation `self**other` and flag if there was an overflow + fn overflowing_pow(self, other: Self) -> (Self, bool); } macro_rules! construct_uint { @@ -96,14 +121,12 @@ macro_rules! construct_uint { )) } - /// Conversion to u32 #[inline] fn low_u32(&self) -> u32 { let &$name(ref arr) = self; arr[0] as u32 } - /// Conversion to u64 #[inline] fn low_u64(&self) -> u64 { let &$name(ref arr) = self; @@ -131,6 +154,7 @@ macro_rules! construct_uint { } arr[0] } + /// Return the least number of bits needed to represent the number #[inline] fn bits(&self) -> usize { @@ -164,27 +188,82 @@ macro_rules! construct_uint { } #[inline] - fn exp10(n: usize) -> $name { + fn exp10(n: usize) -> Self { match n { - 0 => $name::from(1u64), - _ => $name::exp10(n - 1) * $name::from(10u64) + 0 => Self::from(1u64), + _ => Self::exp10(n - 1) * Self::from(10u64) } } #[inline] - fn zero() -> $name { + fn zero() -> Self { From::from(0u64) } #[inline] - fn one() -> $name { + fn one() -> Self { From::from(1u64) } + + /// Fast exponentation by squaring + /// https://en.wikipedia.org/wiki/Exponentiation_by_squaring + fn pow(self, expon: Self) -> Self { + if expon == Self::zero() { + return Self::one() + } + let is_even = |x : &Self| x.low_u64() & 1 == 0; + + let u_one = Self::one(); + let u_two = Self::from(2); + let mut y = u_one; + let mut n = expon; + let mut x = self; + while n > u_one { + if is_even(&n) { + x = x * x; + n = n / u_two; + } else { + y = x * y; + x = x * x; + n = (n - u_one) / u_two; + } + } + x * y + } + + /// Fast exponentation by squaring + /// https://en.wikipedia.org/wiki/Exponentiation_by_squaring + fn overflowing_pow(self, expon: Self) -> (Self, bool) { + if expon == Self::zero() { + return (Self::one(), false) + } + let is_even = |x : &Self| x.low_u64() & 1 == 0; + + let u_one = Self::one(); + let u_two = Self::from(2); + let mut y = u_one; + let mut n = expon; + let mut x = self; + let mut overflow = false; + + while n > u_one { + if is_even(&n) { + x = overflowing!(x.overflowing_mul(x), overflow); + n = n / u_two; + } else { + y = overflowing!(x.overflowing_mul(y), overflow); + x = overflowing!(x.overflowing_mul(x), overflow); + n = (n - u_one) / u_two; + } + } + let res = overflowing!(x.overflowing_mul(y), overflow); + (res, overflow) + } } impl $name { /// Multiplication by u32 - fn mul_u32(self, other: u32) -> $name { + fn mul_u32(self, other: u32) -> Self { let $name(ref arr) = self; let mut carry = [0u64; $n_words]; let mut ret = [0u64; $n_words]; @@ -205,7 +284,7 @@ macro_rules! construct_uint { } /// Overflowing multiplication by u32 - fn overflowing_mul_u32(self, other: u32) -> ($name, bool) { + fn overflowing_mul_u32(self, other: u32) -> (Self, bool) { let $name(ref arr) = self; let mut carry = [0u64; $n_words]; let mut ret = [0u64; $n_words]; @@ -225,8 +304,11 @@ macro_rules! construct_uint { overflow = true } } - let (result, add_overflow) = $name(ret).overflowing_add($name(carry)); - (result, add_overflow || overflow) + let result = overflowing!( + $name(ret).overflowing_add($name(carry)), + overflow + ); + (result, overflow) } } @@ -325,21 +407,21 @@ macro_rules! construct_uint { carry[i + 1] = 1; b_carry = true; } else { - overflow = true + overflow = true; } } } - if b_carry { - let (ret, add_overflow) = $name(ret).overflowing_add($name(carry)); - (ret, add_overflow || overflow) + if b_carry { + let ret = overflowing!($name(ret).overflowing_add($name(carry)), overflow); + (ret, overflow) } else { ($name(ret), overflow) } } fn overflowing_sub(self, other: $name) -> ($name, bool) { - let (res, _overflow) = (!other).overflowing_add(From::from(1u64)); - let (res, _overflow) = self.overflowing_add(res); + let res = overflowing!((!other).overflowing_add(From::from(1u64))); + let res = overflowing!(self.overflowing_add(res)); (res, self < other) } @@ -348,10 +430,9 @@ macro_rules! construct_uint { let mut overflow = false; // TODO: be more efficient about this for i in 0..(2 * $n_words) { - let (v, mul_overflow) = self.overflowing_mul_u32((other >> (32 * i)).low_u32()); - let (new_res, add_overflow) = res.overflowing_add(v << (32 * i)); - res = new_res; - overflow = overflow || mul_overflow || add_overflow; + let v = overflowing!(self.overflowing_mul_u32((other >> (32 * i)).low_u32()), overflow); + let res2 = overflowing!(v.overflowing_shl(32 * i as u32), overflow); + res = overflowing!(res.overflowing_add(res2), overflow); } (res, overflow) } @@ -368,9 +449,38 @@ macro_rules! construct_uint { (!self, true) } - fn overflowing_shl(self, _shift32: u32) -> ($name, bool) { - // TODO [todr] not used for now - unimplemented!(); + fn overflowing_shl(self, shift32: u32) -> ($name, bool) { + let $name(ref original) = self; + let mut ret = [0u64; $n_words]; + let shift = shift32 as usize; + let word_shift = shift / 64; + let bit_shift = shift % 64; + for i in 0..$n_words { + // Shift + if i + word_shift < $n_words { + ret[i + word_shift] += original[i] << bit_shift; + } + // Carry + if bit_shift > 0 && i + word_shift + 1 < $n_words { + ret[i + word_shift + 1] += original[i] >> (64 - bit_shift); + } + } + // Detecting overflow + let last = $n_words - word_shift - if bit_shift > 0 { 1 } else { 0 }; + let overflow = if bit_shift > 0 { + (original[last] >> (64 - bit_shift)) > 0 + } else if word_shift > 0 { + original[last] > 0 + } else { + false + }; + + for i in last+1..$n_words-1 { + if original[i] > 0 { + return ($name(ret), true); + } + } + ($name(ret), overflow) } fn overflowing_shr(self, _shift32: u32) -> ($name, bool) { @@ -409,9 +519,8 @@ macro_rules! construct_uint { #[inline] fn sub(self, other: $name) -> $name { panic_on_overflow!(self < other); - let (res, _overflow) = (!other).overflowing_add(From::from(1u64)); - let (res, _overflow) = self.overflowing_add(res); - res + let res = overflowing!((!other).overflowing_add(From::from(1u64))); + overflowing!(self.overflowing_add(res)) } } @@ -422,7 +531,10 @@ macro_rules! construct_uint { let mut res = $name::from(0u64); // TODO: be more efficient about this for i in 0..(2 * $n_words) { - res = res + (self.mul_u32((other >> (32 * i)).low_u32()) << (32 * i)); + let v = self.mul_u32((other >> (32 * i)).low_u32()); + let (r, overflow) = v.overflowing_shl(32 * i as u32); + panic_on_overflow!(overflow); + res = res + r; } res } @@ -453,8 +565,7 @@ macro_rules! construct_uint { loop { if sub_copy >= shift_copy { ret[shift / 64] |= 1 << (shift % 64); - let (copy, _overflow) = sub_copy.overflowing_sub(shift_copy); - sub_copy = copy + sub_copy = overflowing!(sub_copy.overflowing_sub(shift_copy)); } shift_copy = shift_copy >> 1; if shift == 0 { break; } @@ -868,7 +979,7 @@ mod tests { let incr = shr + U256::from(1u64); assert_eq!(incr, U256([0x7DDE000000000001u64, 0x0001BD5B7DDFBD5B, 0, 0])); // Subtraction - let (sub, _of) = incr.overflowing_sub(init); + let sub = overflowing!(incr.overflowing_sub(init)); assert_eq!(sub, U256([0x9F30411021524112u64, 0x0001BD5B7DDFBD5A, 0, 0])); // Multiplication let mult = sub.mul_u32(300); @@ -915,11 +1026,48 @@ mod tests { assert_eq!(U256::from(1000u64).mul_u32(50), U256::from(50000u64)); } + #[test] + fn uint256_pow () { + assert_eq!(U256::from(10).pow(U256::from(0)), U256::from(1)); + assert_eq!(U256::from(10).pow(U256::from(1)), U256::from(10)); + assert_eq!(U256::from(10).pow(U256::from(2)), U256::from(100)); + assert_eq!(U256::from(10).pow(U256::from(3)), U256::from(1000)); + assert_eq!(U256::from(10).pow(U256::from(20)), U256::exp10(20)); + } + + #[test] + #[should_panic] + fn uint256_pow_overflow_panic () { + U256::from(2).pow(U256::from(0x100)); + } + + #[test] + fn uint256_overflowing_pow () { + // assert_eq!( + // U256::from(2).overflowing_pow(U256::from(0xff)), + // (U256::from_str("8000000000000000000000000000000000000000000000000000000000000000").unwrap(), false) + // ); + assert_eq!( + U256::from(2).overflowing_pow(U256::from(0x100)), + (U256::zero(), true) + ); + } + #[test] pub fn uint256_mul1() { assert_eq!(U256::from(1u64) * U256::from(10u64), U256::from(10u64)); } + #[test] + pub fn uint256_overflowing_mul() { + assert_eq!( + U256::from_str("100000000000000000000000000000000").unwrap().overflowing_mul( + U256::from_str("100000000000000000000000000000000").unwrap() + ), + (U256::zero(), true) + ); + } + #[test] pub fn uint128_add() { assert_eq!( @@ -972,9 +1120,11 @@ mod tests { U256::from_str("7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff").unwrap() ), (U256::from_str("1").unwrap(), true) - ); + ); } + + #[test] #[should_panic] pub fn uint256_mul_overflow_panic() { @@ -1002,7 +1152,6 @@ mod tests { U256::from_str("1").unwrap(); } - #[ignore] #[test] pub fn uint256_shl_overflow() { assert_eq!( @@ -1012,9 +1161,41 @@ mod tests { ); } - #[ignore] #[test] - #[should_panic] + pub fn uint256_shl_overflow_words() { + assert_eq!( + U256::from_str("0000000000000001ffffffffffffffffffffffffffffffffffffffffffffffff").unwrap() + .overflowing_shl(64), + (U256::from_str("ffffffffffffffffffffffffffffffffffffffffffffffff0000000000000000").unwrap(), true) + ); + assert_eq!( + U256::from_str("0000000000000000ffffffffffffffffffffffffffffffffffffffffffffffff").unwrap() + .overflowing_shl(64), + (U256::from_str("ffffffffffffffffffffffffffffffffffffffffffffffff0000000000000000").unwrap(), false) + ); + } + + #[test] + pub fn uint256_shl_overflow_words2() { + assert_eq!( + U256::from_str("00000000000000000000000000000001ffffffffffffffffffffffffffffffff").unwrap() + .overflowing_shl(128), + (U256::from_str("ffffffffffffffffffffffffffffffff00000000000000000000000000000000").unwrap(), true) + ); + assert_eq!( + U256::from_str("00000000000000000000000000000000ffffffffffffffffffffffffffffffff").unwrap() + .overflowing_shl(128), + (U256::from_str("ffffffffffffffffffffffffffffffff00000000000000000000000000000000").unwrap(), false) + ); + assert_eq!( + U256::from_str("00000000000000000000000000000000ffffffffffffffffffffffffffffffff").unwrap() + .overflowing_shl(129), + (U256::from_str("fffffffffffffffffffffffffffffffe00000000000000000000000000000000").unwrap(), true) + ); + } + + + #[test] pub fn uint256_shl_overflow2() { assert_eq!( U256::from_str("0fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff").unwrap()