// SPDX-License-Identifier: CC0-1.0 //! Proof-of-work related integer types. //! //! Provides the [`Work`] and [`Target`] types that are used in proof-of-work calculations. The //! functions here are designed to be fast, by that we mean it is safe to use them to check headers. //! use core::fmt::{self, LowerHex, UpperHex}; use core::ops::{Add, Div, Mul, Not, Rem, Shl, Shr, Sub}; use io::{BufRead, Write}; #[cfg(all(test, mutate))] use mutagen::mutate; use units::parse; use crate::blockdata::block::BlockHash; use crate::consensus::encode::{self, Decodable, Encodable}; #[cfg(doc)] use crate::consensus::Params; use crate::error::{ContainsPrefixError, MissingPrefixError, PrefixedHexError, UnprefixedHexError}; use crate::Network; /// Implement traits and methods shared by `Target` and `Work`. macro_rules! do_impl { ($ty:ident) => { impl $ty { /// Creates `Self` from a big-endian byte array. #[inline] pub fn from_be_bytes(bytes: [u8; 32]) -> $ty { $ty(U256::from_be_bytes(bytes)) } /// Creates `Self` from a little-endian byte array. #[inline] pub fn from_le_bytes(bytes: [u8; 32]) -> $ty { $ty(U256::from_le_bytes(bytes)) } /// Converts `self` to a big-endian byte array. #[inline] pub fn to_be_bytes(self) -> [u8; 32] { self.0.to_be_bytes() } /// Converts `self` to a little-endian byte array. #[inline] pub fn to_le_bytes(self) -> [u8; 32] { self.0.to_le_bytes() } } impl fmt::Display for $ty { #[inline] fn fmt(&self, f: &mut fmt::Formatter) -> core::fmt::Result { fmt::Display::fmt(&self.0, f) } } impl fmt::LowerHex for $ty { #[inline] fn fmt(&self, f: &mut fmt::Formatter) -> core::fmt::Result { fmt::LowerHex::fmt(&self.0, f) } } impl fmt::UpperHex for $ty { #[inline] fn fmt(&self, f: &mut fmt::Formatter) -> core::fmt::Result { fmt::UpperHex::fmt(&self.0, f) } } }; } /// A 256 bit integer representing work. /// /// Work is a measure of how difficult it is to find a hash below a given [`Target`]. #[derive(Copy, Clone, Debug, PartialEq, Eq, PartialOrd, Ord, Hash)] #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))] #[cfg_attr(feature = "serde", serde(crate = "actual_serde"))] pub struct Work(U256); impl Work { /// Converts this [`Work`] to [`Target`]. pub fn to_target(self) -> Target { Target(self.0.inverse()) } /// Returns log2 of this work. /// /// The result inherently suffers from a loss of precision and is, therefore, meant to be /// used mainly for informative and displaying purposes, similarly to Bitcoin Core's /// `log2_work` output in its logs. #[cfg(feature = "std")] pub fn log2(self) -> f64 { self.0.to_f64().log2() } } do_impl!(Work); impl Add for Work { type Output = Work; fn add(self, rhs: Self) -> Self { Work(self.0 + rhs.0) } } impl Sub for Work { type Output = Work; fn sub(self, rhs: Self) -> Self { Work(self.0 - rhs.0) } } /// A 256 bit integer representing target. /// /// The SHA-256 hash of a block's header must be lower than or equal to the current target for the /// block to be accepted by the network. The lower the target, the more difficult it is to generate /// a block. (See also [`Work`].) /// /// ref: #[derive(Copy, Clone, Debug, PartialEq, Eq, PartialOrd, Ord, Hash)] #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))] #[cfg_attr(feature = "serde", serde(crate = "actual_serde"))] pub struct Target(U256); impl Target { /// When parsing nBits, Bitcoin Core converts a negative target threshold into a target of zero. pub const ZERO: Target = Target(U256::ZERO); /// The maximum possible target. /// /// This value is used to calculate difficulty, which is defined as how difficult the current /// target makes it to find a block relative to how difficult it would be at the highest /// possible target. Remember highest target == lowest difficulty. /// /// ref: // In Bitcoind this is ~(u256)0 >> 32 stored as a floating-point type so it gets truncated, hence // the low 208 bits are all zero. pub const MAX: Self = Target(U256(0xFFFF_u128 << (208 - 128), 0)); /// The maximum **attainable** target value on mainnet. /// /// Not all target values are attainable because consensus code uses the compact format to /// represent targets (see [`CompactTarget`]). pub const MAX_ATTAINABLE_MAINNET: Self = Target(U256(0xFFFF_u128 << (208 - 128), 0)); /// The proof of work limit on testnet. // Taken from Bitcoin Core but had lossy conversion to/from compact form. // https://github.com/bitcoin/bitcoin/blob/8105bce5b384c72cf08b25b7c5343622754e7337/src/kernel/chainparams.cpp#L208 pub const MAX_ATTAINABLE_TESTNET: Self = Target(U256(0xFFFF_u128 << (208 - 128), 0)); /// The proof of work limit on regtest. // Taken from Bitcoin Core but had lossy conversion to/from compact form. // https://github.com/bitcoin/bitcoin/blob/8105bce5b384c72cf08b25b7c5343622754e7337/src/kernel/chainparams.cpp#L411 pub const MAX_ATTAINABLE_REGTEST: Self = Target(U256(0x7FFF_FF00u128 << 96, 0)); /// The proof of work limit on signet. // Taken from Bitcoin Core but had lossy conversion to/from compact form. // https://github.com/bitcoin/bitcoin/blob/8105bce5b384c72cf08b25b7c5343622754e7337/src/kernel/chainparams.cpp#L348 pub const MAX_ATTAINABLE_SIGNET: Self = Target(U256(0x0377_ae00 << 80, 0)); /// Computes the [`Target`] value from a compact representation. /// /// ref: pub fn from_compact(c: CompactTarget) -> Target { let bits = c.0; // This is a floating-point "compact" encoding originally used by // OpenSSL, which satoshi put into consensus code, so we're stuck // with it. The exponent needs to have 3 subtracted from it, hence // this goofy decoding code. 3 is due to 3 bytes in the mantissa. let (mant, expt) = { let unshifted_expt = bits >> 24; if unshifted_expt <= 3 { ((bits & 0xFFFFFF) >> (8 * (3 - unshifted_expt as usize)), 0) } else { (bits & 0xFFFFFF, 8 * ((bits >> 24) - 3)) } }; // The mantissa is signed but may not be negative. if mant > 0x7F_FFFF { Target::ZERO } else { Target(U256::from(mant) << expt) } } /// Computes the compact value from a [`Target`] representation. /// /// The compact form is by definition lossy, this means that /// `t == Target::from_compact(t.to_compact_lossy())` does not always hold. pub fn to_compact_lossy(self) -> CompactTarget { let mut size = (self.0.bits() + 7) / 8; let mut compact = if size <= 3 { (self.0.low_u64() << (8 * (3 - size))) as u32 } else { let bn = self.0 >> (8 * (size - 3)); bn.low_u32() }; if (compact & 0x0080_0000) != 0 { compact >>= 8; size += 1; } CompactTarget(compact | (size << 24)) } /// Returns true if block hash is less than or equal to this [`Target`]. /// /// Proof-of-work validity for a block requires the hash of the block to be less than or equal /// to the target. #[cfg_attr(all(test, mutate), mutate)] pub fn is_met_by(&self, hash: BlockHash) -> bool { use hashes::Hash; let hash = U256::from_le_bytes(hash.to_byte_array()); hash <= self.0 } /// Converts this [`Target`] to [`Work`]. /// /// "Work" is defined as the work done to mine a block with this target value (recorded in the /// block header in compact form as nBits). This is not the same as the difficulty to mine a /// block with this target (see `Self::difficulty`). pub fn to_work(self) -> Work { Work(self.0.inverse()) } /// Computes the popular "difficulty" measure for mining. /// /// Difficulty represents how difficult the current target makes it to find a block, relative to /// how difficult it would be at the highest possible target (highest target == lowest difficulty). /// /// For example, a difficulty of 6,695,826 means that at a given hash rate, it will, on average, /// take ~6.6 million times as long to find a valid block as it would at a difficulty of 1, or /// alternatively, it will take, again on average, ~6.6 million times as many hashes to find a /// valid block /// /// # Note /// /// Difficulty is calculated using the following algorithm `max / current` where [max] is /// defined for the Bitcoin network and `current` is the current [target] for this block. As /// such, a low target implies a high difficulty. Since [`Target`] is represented as a 256 bit /// integer but `difficulty()` returns only 128 bits this means for targets below approximately /// `0xffff_ffff_ffff_ffff_ffff_ffff` `difficulty()` will saturate at `u128::MAX`. /// /// [max]: Target::max /// [target]: crate::blockdata::block::Header::target #[cfg_attr(all(test, mutate), mutate)] pub fn difficulty(&self, network: Network) -> u128 { let max = match network { Network::Bitcoin => Target::MAX_ATTAINABLE_MAINNET, Network::Testnet => Target::MAX_ATTAINABLE_TESTNET, Network::Signet => Target::MAX_ATTAINABLE_SIGNET, Network::Regtest => Target::MAX_ATTAINABLE_REGTEST, }; let d = max.0 / self.0; d.saturating_to_u128() } /// Computes the popular "difficulty" measure for mining and returns a float value of f64. /// /// See [`difficulty`] for details. /// /// # Returns /// /// Returns [`f64::INFINITY`] if `self` is zero (caused by divide by zero). /// /// [`difficulty`]: Target::difficulty #[cfg_attr(all(test, mutate), mutate)] pub fn difficulty_float(&self) -> f64 { TARGET_MAX_F64 / self.0.to_f64() } /// Computes the minimum valid [`Target`] threshold allowed for a block in which a difficulty /// adjustment occurs. /// /// The difficulty can only decrease or increase by a factor of 4 max on each difficulty /// adjustment period. pub fn min_difficulty_transition_threshold(&self) -> Self { Self(self.0 >> 2) } /// Computes the maximum valid [`Target`] threshold allowed for a block in which a difficulty /// adjustment occurs. /// /// The difficulty can only decrease or increase by a factor of 4 max on each difficulty /// adjustment period. pub fn max_difficulty_transition_threshold(&self) -> Self { Self(self.0 << 2) } } do_impl!(Target); /// Encoding of 256-bit target as 32-bit float. /// /// This is used to encode a target into the block header. Satoshi made this part of consensus code /// in the original version of Bitcoin, likely copying an idea from OpenSSL. /// /// OpenSSL's bignum (BN) type has an encoding, which is even called "compact" as in bitcoin, which /// is exactly this format. #[derive(Copy, Clone, Debug, Default, PartialEq, Eq, PartialOrd, Ord, Hash)] #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))] #[cfg_attr(feature = "serde", serde(crate = "actual_serde"))] pub struct CompactTarget(u32); impl CompactTarget { /// Creates a `CompactTarget` from an prefixed hex string. pub fn from_hex(s: &str) -> Result { let stripped = if let Some(stripped) = s.strip_prefix("0x") { stripped } else if let Some(stripped) = s.strip_prefix("0X") { stripped } else { return Err(MissingPrefixError::new(s).into()); }; let target = parse::hex_u32(stripped)?; Ok(Self::from_consensus(target)) } /// Creates a `CompactTarget` from an unprefixed hex string. pub fn from_unprefixed_hex(s: &str) -> Result { if s.starts_with("0x") || s.starts_with("0X") { return Err(ContainsPrefixError::new(s).into()); } let lock_time = parse::hex_u32(s)?; Ok(Self::from_consensus(lock_time)) } /// Creates a [`CompactTarget`] from a consensus encoded `u32`. pub fn from_consensus(bits: u32) -> Self { Self(bits) } /// Returns the consensus encoded `u32` representation of this [`CompactTarget`]. pub fn to_consensus(self) -> u32 { self.0 } } impl From for Target { fn from(c: CompactTarget) -> Self { Target::from_compact(c) } } impl Encodable for CompactTarget { #[inline] fn consensus_encode(&self, w: &mut W) -> Result { self.0.consensus_encode(w) } } impl Decodable for CompactTarget { #[inline] fn consensus_decode(r: &mut R) -> Result { u32::consensus_decode(r).map(CompactTarget) } } impl LowerHex for CompactTarget { #[inline] fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { LowerHex::fmt(&self.0, f) } } impl UpperHex for CompactTarget { #[inline] fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { UpperHex::fmt(&self.0, f) } } /// Big-endian 256 bit integer type. // (high, low): u.0 contains the high bits, u.1 contains the low bits. #[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Hash, Default)] struct U256(u128, u128); impl U256 { const MAX: U256 = U256(0xffff_ffff_ffff_ffff_ffff_ffff_ffff_ffff, 0xffff_ffff_ffff_ffff_ffff_ffff_ffff_ffff); const ZERO: U256 = U256(0, 0); const ONE: U256 = U256(0, 1); /// Creates [`U256`] from a big-endian array of `u8`s. #[cfg_attr(all(test, mutate), mutate)] fn from_be_bytes(a: [u8; 32]) -> U256 { let (high, low) = split_in_half(a); let big = u128::from_be_bytes(high); let little = u128::from_be_bytes(low); U256(big, little) } /// Creates a [`U256`] from a little-endian array of `u8`s. #[cfg_attr(all(test, mutate), mutate)] fn from_le_bytes(a: [u8; 32]) -> U256 { let (high, low) = split_in_half(a); let little = u128::from_le_bytes(high); let big = u128::from_le_bytes(low); U256(big, little) } /// Converts `Self` to a big-endian array of `u8`s. #[cfg_attr(all(test, mutate), mutate)] fn to_be_bytes(self) -> [u8; 32] { let mut out = [0; 32]; out[..16].copy_from_slice(&self.0.to_be_bytes()); out[16..].copy_from_slice(&self.1.to_be_bytes()); out } /// Converts `Self` to a little-endian array of `u8`s. #[cfg_attr(all(test, mutate), mutate)] fn to_le_bytes(self) -> [u8; 32] { let mut out = [0; 32]; out[..16].copy_from_slice(&self.1.to_le_bytes()); out[16..].copy_from_slice(&self.0.to_le_bytes()); out } /// Calculates 2^256 / (x + 1) where x is a 256 bit unsigned integer. /// /// 2**256 / (x + 1) == ~x / (x + 1) + 1 /// /// (Equation shamelessly stolen from bitcoind) fn inverse(&self) -> U256 { // We should never have a target/work of zero so this doesn't matter // that much but we define the inverse of 0 as max. if self.is_zero() { return U256::MAX; } // We define the inverse of 1 as max. if self.is_one() { return U256::MAX; } // We define the inverse of max as 1. if self.is_max() { return U256::ONE; } let ret = !*self / self.wrapping_inc(); ret.wrapping_inc() } #[cfg_attr(all(test, mutate), mutate)] fn is_zero(&self) -> bool { self.0 == 0 && self.1 == 0 } #[cfg_attr(all(test, mutate), mutate)] fn is_one(&self) -> bool { self.0 == 0 && self.1 == 1 } #[cfg_attr(all(test, mutate), mutate)] fn is_max(&self) -> bool { self.0 == u128::MAX && self.1 == u128::MAX } /// Returns the low 32 bits. fn low_u32(&self) -> u32 { self.low_u128() as u32 } /// Returns the low 64 bits. fn low_u64(&self) -> u64 { self.low_u128() as u64 } /// Returns the low 128 bits. fn low_u128(&self) -> u128 { self.1 } /// Returns `self` as a `u128` saturating to `u128::MAX` if `self` is too big. // Matagen gives false positive because >= and > both return u128::MAX fn saturating_to_u128(&self) -> u128 { if *self > U256::from(u128::MAX) { u128::MAX } else { self.low_u128() } } /// Returns the least number of bits needed to represent the number. #[cfg_attr(all(test, mutate), mutate)] fn bits(&self) -> u32 { if self.0 > 0 { 256 - self.0.leading_zeros() } else { 128 - self.1.leading_zeros() } } /// Wrapping multiplication by `u64`. /// /// # Returns /// /// The multiplication result along with a boolean indicating whether an arithmetic overflow /// occurred. If an overflow occurred then the wrapped value is returned. // mutagen false pos mul_u64: replace `|` with `^` (XOR is same as OR when combined with <<) // mutagen false pos mul_u64: replace `|` with `^` #[cfg_attr(all(test, mutate), mutate)] fn mul_u64(self, rhs: u64) -> (U256, bool) { let mut carry: u128 = 0; let mut split_le = [self.1 as u64, (self.1 >> 64) as u64, self.0 as u64, (self.0 >> 64) as u64]; for word in &mut split_le { // This will not overflow, for proof see https://github.com/rust-bitcoin/rust-bitcoin/pull/1496#issuecomment-1365938572 let n = carry + u128::from(rhs) * u128::from(*word); *word = n as u64; // Intentional truncation, save the low bits carry = n >> 64; // and carry the high bits. } let low = u128::from(split_le[0]) | u128::from(split_le[1]) << 64; let high = u128::from(split_le[2]) | u128::from(split_le[3]) << 64; (Self(high, low), carry != 0) } /// Calculates quotient and remainder. /// /// # Returns /// /// (quotient, remainder) /// /// # Panics /// /// If `rhs` is zero. #[cfg_attr(all(test, mutate), mutate)] fn div_rem(self, rhs: Self) -> (Self, Self) { let mut sub_copy = self; let mut shift_copy = rhs; let mut ret = [0u128; 2]; let my_bits = self.bits(); let your_bits = rhs.bits(); // Check for division by 0 assert!(your_bits != 0, "attempted to divide {} by zero", self); // Early return in case we are dividing by a larger number than us if my_bits < your_bits { return (U256::ZERO, sub_copy); } // Bitwise long division let mut shift = my_bits - your_bits; shift_copy = shift_copy << shift; loop { if sub_copy >= shift_copy { ret[1 - (shift / 128) as usize] |= 1 << (shift % 128); sub_copy = sub_copy.wrapping_sub(shift_copy); } shift_copy = shift_copy >> 1; if shift == 0 { break; } shift -= 1; } (U256(ret[0], ret[1]), sub_copy) } /// Calculates `self` + `rhs` /// /// Returns a tuple of the addition along with a boolean indicating whether an arithmetic /// overflow would occur. If an overflow would have occurred then the wrapped value is returned. #[must_use = "this returns the result of the operation, without modifying the original"] #[cfg_attr(all(test, mutate), mutate)] fn overflowing_add(self, rhs: Self) -> (Self, bool) { let mut ret = U256::ZERO; let mut ret_overflow = false; let (high, overflow) = self.0.overflowing_add(rhs.0); ret.0 = high; ret_overflow |= overflow; let (low, overflow) = self.1.overflowing_add(rhs.1); ret.1 = low; if overflow { let (high, overflow) = ret.0.overflowing_add(1); ret.0 = high; ret_overflow |= overflow; } (ret, ret_overflow) } /// Calculates `self` - `rhs` /// /// Returns a tuple of the subtraction along with a boolean indicating whether an arithmetic /// overflow would occur. If an overflow would have occurred then the wrapped value is returned. #[must_use = "this returns the result of the operation, without modifying the original"] #[cfg_attr(all(test, mutate), mutate)] fn overflowing_sub(self, rhs: Self) -> (Self, bool) { let ret = self.wrapping_add(!rhs).wrapping_add(Self::ONE); let overflow = rhs > self; (ret, overflow) } /// Calculates the multiplication of `self` and `rhs`. /// /// Returns a tuple of the multiplication along with a boolean /// indicating whether an arithmetic overflow would occur. If an /// overflow would have occurred then the wrapped value is returned. #[must_use = "this returns the result of the operation, without modifying the original"] #[cfg_attr(all(test, mutate), mutate)] fn overflowing_mul(self, rhs: Self) -> (Self, bool) { let mut ret = U256::ZERO; let mut ret_overflow = false; for i in 0..3 { let to_mul = (rhs >> (64 * i)).low_u64(); let (mul_res, _) = self.mul_u64(to_mul); ret = ret.wrapping_add(mul_res << (64 * i)); } let to_mul = (rhs >> 192).low_u64(); let (mul_res, overflow) = self.mul_u64(to_mul); ret_overflow |= overflow; let (sum, overflow) = ret.overflowing_add(mul_res); ret = sum; ret_overflow |= overflow; (ret, ret_overflow) } /// Wrapping (modular) addition. Computes `self + rhs`, wrapping around at the boundary of the /// type. #[must_use = "this returns the result of the operation, without modifying the original"] fn wrapping_add(self, rhs: Self) -> Self { let (ret, _overflow) = self.overflowing_add(rhs); ret } /// Wrapping (modular) subtraction. Computes `self - rhs`, wrapping around at the boundary of /// the type. #[must_use = "this returns the result of the operation, without modifying the original"] fn wrapping_sub(self, rhs: Self) -> Self { let (ret, _overflow) = self.overflowing_sub(rhs); ret } /// Wrapping (modular) multiplication. Computes `self * rhs`, wrapping around at the boundary of /// the type. #[must_use = "this returns the result of the operation, without modifying the original"] #[cfg(test)] fn wrapping_mul(self, rhs: Self) -> Self { let (ret, _overflow) = self.overflowing_mul(rhs); ret } /// Returns `self` incremented by 1 wrapping around at the boundary of the type. #[must_use = "this returns the result of the increment, without modifying the original"] #[cfg_attr(all(test, mutate), mutate)] fn wrapping_inc(&self) -> U256 { let mut ret = U256::ZERO; ret.1 = self.1.wrapping_add(1); if ret.1 == 0 { ret.0 = self.0.wrapping_add(1); } else { ret.0 = self.0; } ret } /// Panic-free bitwise shift-left; yields `self << mask(rhs)`, where `mask` removes any /// high-order bits of `rhs` that would cause the shift to exceed the bitwidth of the type. /// /// Note that this is *not* the same as a rotate-left; the RHS of a wrapping shift-left is /// restricted to the range of the type, rather than the bits shifted out of the LHS being /// returned to the other end. We do not currently support `rotate_left`. #[must_use = "this returns the result of the operation, without modifying the original"] #[cfg_attr(all(test, mutate), mutate)] fn wrapping_shl(self, rhs: u32) -> Self { let shift = rhs & 0x000000ff; let mut ret = U256::ZERO; let word_shift = shift >= 128; let bit_shift = shift % 128; if word_shift { ret.0 = self.1 << bit_shift } else { ret.0 = self.0 << bit_shift; if bit_shift > 0 { ret.0 += self.1.wrapping_shr(128 - bit_shift); } ret.1 = self.1 << bit_shift; } ret } /// Panic-free bitwise shift-right; yields `self >> mask(rhs)`, where `mask` removes any /// high-order bits of `rhs` that would cause the shift to exceed the bitwidth of the type. /// /// Note that this is *not* the same as a rotate-right; the RHS of a wrapping shift-right is /// restricted to the range of the type, rather than the bits shifted out of the LHS being /// returned to the other end. We do not currently support `rotate_right`. #[must_use = "this returns the result of the operation, without modifying the original"] #[cfg_attr(all(test, mutate), mutate)] fn wrapping_shr(self, rhs: u32) -> Self { let shift = rhs & 0x000000ff; let mut ret = U256::ZERO; let word_shift = shift >= 128; let bit_shift = shift % 128; if word_shift { ret.1 = self.0 >> bit_shift } else { ret.0 = self.0 >> bit_shift; ret.1 = self.1 >> bit_shift; if bit_shift > 0 { ret.1 += self.0.wrapping_shl(128 - bit_shift); } } ret } /// Format `self` to `f` as a decimal when value is known to be non-zero. fn fmt_decimal(&self, f: &mut fmt::Formatter) -> fmt::Result { const DIGITS: usize = 78; // U256::MAX has 78 base 10 digits. const TEN: U256 = U256(0, 10); let mut buf = [0_u8; DIGITS]; let mut i = DIGITS - 1; // We loop backwards. let mut cur = *self; loop { let digit = (cur % TEN).low_u128() as u8; // Cast after rem 10 is lossless. buf[i] = digit + b'0'; cur = cur / TEN; if cur.is_zero() { break; } i -= 1; } let s = core::str::from_utf8(&buf[i..]).expect("digits 0-9 are valid UTF8"); f.pad_integral(true, "", s) } /// Convert self to f64. #[inline] fn to_f64(self) -> f64 { // Reference: https://blog.m-ou.se/floats/ // Step 1: Get leading zeroes let leading_zeroes = 256 - self.bits(); // Step 2: Get msb to be farthest left bit let left_aligned = self.wrapping_shl(leading_zeroes); // Step 3: Shift msb to fit in lower 53 bits (128-53=75) to get the mantissa // * Shifting the border of the 2 u128s to line up with mantissa and dropped bits let middle_aligned = left_aligned >> 75; // * This is the 53 most significant bits as u128 let mantissa = middle_aligned.0; // Step 4: Dropped bits (except for last 75 bits) are all in the second u128. // Bitwise OR the rest of the bits into it, preserving the highest bit, // so we take the lower 75 bits of middle_aligned.1 and mix it in. (See blog for explanation) let dropped_bits = middle_aligned.1 | (left_aligned.1 & 0x7FF_FFFF_FFFF_FFFF_FFFF); // Step 5: The msb of the dropped bits has been preserved, and all other bits // if any were set, would be set somewhere in the other 127 bits. // If msb of dropped bits is 0, it is mantissa + 0 // If msb of dropped bits is 1, it is mantissa + 0 only if mantissa lowest bit is 0 // and other bits of the dropped bits are all 0. // (This is why we only care if the other non-msb dropped bits are all 0 or not, // so we can just OR them to make sure any bits show up somewhere.) let mantissa = (mantissa + ((dropped_bits - (dropped_bits >> 127 & !mantissa)) >> 127)) as u64; // Step 6: Calculate the exponent // If self is 0, exponent should be 0 (special meaning) and mantissa will end up 0 too // Otherwise, (255 - n) + 1022 so it simplifies to 1277 - n // 1023 and 1022 are the cutoffs for the exponent having the msb next to the decimal point let exponent = if self == Self::ZERO { 0 } else { 1277 - leading_zeroes as u64 }; // Step 7: sign bit is always 0, exponent is shifted into place // Use addition instead of bitwise OR to saturate the exponent if mantissa overflows f64::from_bits((exponent << 52) + mantissa) } } // Target::MAX as a float value. Calculated with U256::to_f64. // This is validated in the unit tests as well. const TARGET_MAX_F64: f64 = 2.695953529101131e67; impl> From for U256 { fn from(x: T) -> Self { U256(0, x.into()) } } impl Add for U256 { type Output = Self; fn add(self, rhs: Self) -> Self { let (res, overflow) = self.overflowing_add(rhs); debug_assert!(!overflow, "Addition of U256 values overflowed"); res } } impl Sub for U256 { type Output = Self; fn sub(self, rhs: Self) -> Self { let (res, overflow) = self.overflowing_sub(rhs); debug_assert!(!overflow, "Subtraction of U256 values overflowed"); res } } impl Mul for U256 { type Output = Self; fn mul(self, rhs: Self) -> Self { let (res, overflow) = self.overflowing_mul(rhs); debug_assert!(!overflow, "Multiplication of U256 values overflowed"); res } } impl Div for U256 { type Output = Self; fn div(self, rhs: Self) -> Self { self.div_rem(rhs).0 } } impl Rem for U256 { type Output = Self; fn rem(self, rhs: Self) -> Self { self.div_rem(rhs).1 } } impl Not for U256 { type Output = Self; fn not(self) -> Self { U256(!self.0, !self.1) } } impl Shl for U256 { type Output = Self; fn shl(self, shift: u32) -> U256 { self.wrapping_shl(shift) } } impl Shr for U256 { type Output = Self; fn shr(self, shift: u32) -> U256 { self.wrapping_shr(shift) } } impl fmt::Display for U256 { fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { if self.is_zero() { f.pad_integral(true, "", "0") } else { self.fmt_decimal(f) } } } impl fmt::Debug for U256 { fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { write!(f, "{:#x}", self) } } macro_rules! impl_hex { ($hex:ident, $case:expr) => { impl $hex for U256 { fn fmt(&self, f: &mut fmt::Formatter) -> core::fmt::Result { hex::fmt_hex_exact!(f, 32, &self.to_be_bytes(), $case) } } }; } impl_hex!(LowerHex, hex::Case::Lower); impl_hex!(UpperHex, hex::Case::Upper); #[cfg(feature = "serde")] impl crate::serde::Serialize for U256 { fn serialize(&self, serializer: S) -> Result where S: crate::serde::Serializer, { struct DisplayHex(U256); impl fmt::Display for DisplayHex { fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { write!(f, "{:x}", self.0) } } if serializer.is_human_readable() { serializer.collect_str(&DisplayHex(*self)) } else { let bytes = self.to_be_bytes(); serializer.serialize_bytes(&bytes) } } } #[cfg(feature = "serde")] impl<'de> crate::serde::Deserialize<'de> for U256 { fn deserialize>(d: D) -> Result { use hex::FromHex; use crate::serde::de; if d.is_human_readable() { struct HexVisitor; impl<'de> de::Visitor<'de> for HexVisitor { type Value = U256; fn expecting(&self, f: &mut fmt::Formatter) -> fmt::Result { f.write_str("a 32 byte ASCII hex string") } fn visit_str(self, s: &str) -> Result where E: de::Error, { if s.len() != 64 { return Err(de::Error::invalid_length(s.len(), &self)); } let b = <[u8; 32]>::from_hex(s) .map_err(|_| de::Error::invalid_value(de::Unexpected::Str(s), &self))?; Ok(U256::from_be_bytes(b)) } fn visit_bytes(self, v: &[u8]) -> Result where E: de::Error, { if let Ok(hex) = core::str::from_utf8(v) { let b = <[u8; 32]>::from_hex(hex).map_err(|_| { de::Error::invalid_value(de::Unexpected::Str(hex), &self) })?; Ok(U256::from_be_bytes(b)) } else { Err(E::invalid_value(::serde::de::Unexpected::Bytes(v), &self)) } } } d.deserialize_str(HexVisitor) } else { struct BytesVisitor; impl<'de> serde::de::Visitor<'de> for BytesVisitor { type Value = U256; fn expecting(&self, f: &mut core::fmt::Formatter) -> core::fmt::Result { f.write_str("a sequence of bytes") } fn visit_bytes(self, v: &[u8]) -> Result where E: serde::de::Error, { let b = v.try_into().map_err(|_| de::Error::invalid_length(v.len(), &self))?; Ok(U256::from_be_bytes(b)) } } d.deserialize_bytes(BytesVisitor) } } } /// Splits a 32 byte array into two 16 byte arrays. fn split_in_half(a: [u8; 32]) -> ([u8; 16], [u8; 16]) { let mut high = [0_u8; 16]; let mut low = [0_u8; 16]; high.copy_from_slice(&a[..16]); low.copy_from_slice(&a[16..]); (high, low) } #[cfg(kani)] impl kani::Arbitrary for U256 { fn any() -> Self { let high: u128 = kani::any(); let low: u128 = kani::any(); Self(high, low) } } #[cfg(test)] mod tests { use super::*; impl> From for Target { fn from(x: T) -> Self { Self(U256::from(x)) } } impl> From for Work { fn from(x: T) -> Self { Self(U256::from(x)) } } impl U256 { fn bit_at(&self, index: usize) -> bool { if index > 255 { panic!("index out of bounds"); } let word = if index < 128 { self.1 } else { self.0 }; (word & (1 << (index % 128))) != 0 } } impl U256 { /// Creates a U256 from a big-endian array of u64's fn from_array(a: [u64; 4]) -> Self { let mut ret = U256::ZERO; ret.0 = (a[0] as u128) << 64 ^ (a[1] as u128); ret.1 = (a[2] as u128) << 64 ^ (a[3] as u128); ret } } #[test] fn u256_num_bits() { assert_eq!(U256::from(255_u64).bits(), 8); assert_eq!(U256::from(256_u64).bits(), 9); assert_eq!(U256::from(300_u64).bits(), 9); assert_eq!(U256::from(60000_u64).bits(), 16); assert_eq!(U256::from(70000_u64).bits(), 17); let u = U256::from(u128::MAX) << 1; assert_eq!(u.bits(), 129); // Try to read the following lines out loud quickly let mut shl = U256::from(70000_u64); shl = shl << 100; assert_eq!(shl.bits(), 117); shl = shl << 100; assert_eq!(shl.bits(), 217); shl = shl << 100; assert_eq!(shl.bits(), 0); } #[test] fn u256_bit_at() { assert!(!U256::from(10_u64).bit_at(0)); assert!(U256::from(10_u64).bit_at(1)); assert!(!U256::from(10_u64).bit_at(2)); assert!(U256::from(10_u64).bit_at(3)); assert!(!U256::from(10_u64).bit_at(4)); let u = U256(0xa000_0000_0000_0000_0000_0000_0000_0000, 0); assert!(u.bit_at(255)); assert!(!u.bit_at(254)); assert!(u.bit_at(253)); assert!(!u.bit_at(252)); } #[test] fn u256_lower_hex() { assert_eq!( format!("{:x}", U256::from(0xDEADBEEF_u64)), "00000000000000000000000000000000000000000000000000000000deadbeef", ); assert_eq!( format!("{:#x}", U256::from(0xDEADBEEF_u64)), "0x00000000000000000000000000000000000000000000000000000000deadbeef", ); assert_eq!( format!("{:x}", U256::MAX), "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff", ); assert_eq!( format!("{:#x}", U256::MAX), "0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff", ); } #[test] fn u256_upper_hex() { assert_eq!( format!("{:X}", U256::from(0xDEADBEEF_u64)), "00000000000000000000000000000000000000000000000000000000DEADBEEF", ); assert_eq!( format!("{:#X}", U256::from(0xDEADBEEF_u64)), "0x00000000000000000000000000000000000000000000000000000000DEADBEEF", ); assert_eq!( format!("{:X}", U256::MAX), "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", ); assert_eq!( format!("{:#X}", U256::MAX), "0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", ); } #[test] fn u256_display() { assert_eq!(format!("{}", U256::from(100_u32)), "100",); assert_eq!(format!("{}", U256::ZERO), "0",); assert_eq!(format!("{}", U256::from(u64::MAX)), format!("{}", u64::MAX),); assert_eq!( format!("{}", U256::MAX), "115792089237316195423570985008687907853269984665640564039457584007913129639935", ); } macro_rules! check_format { ($($test_name:ident, $val:literal, $format_string:literal, $expected:literal);* $(;)?) => { $( #[test] fn $test_name() { assert_eq!(format!($format_string, U256::from($val)), $expected); } )* } } check_format! { check_fmt_0, 0_u32, "{}", "0"; check_fmt_1, 0_u32, "{:2}", " 0"; check_fmt_2, 0_u32, "{:02}", "00"; check_fmt_3, 1_u32, "{}", "1"; check_fmt_4, 1_u32, "{:2}", " 1"; check_fmt_5, 1_u32, "{:02}", "01"; check_fmt_10, 10_u32, "{}", "10"; check_fmt_11, 10_u32, "{:2}", "10"; check_fmt_12, 10_u32, "{:02}", "10"; check_fmt_13, 10_u32, "{:3}", " 10"; check_fmt_14, 10_u32, "{:03}", "010"; check_fmt_20, 1_u32, "{:<2}", "1 "; check_fmt_21, 1_u32, "{:<02}", "01"; check_fmt_22, 1_u32, "{:>2}", " 1"; // This is default but check it anyways. check_fmt_23, 1_u32, "{:>02}", "01"; check_fmt_24, 1_u32, "{:^3}", " 1 "; check_fmt_25, 1_u32, "{:^03}", "001"; // Sanity check, for integral types precision is ignored. check_fmt_30, 0_u32, "{:.1}", "0"; check_fmt_31, 0_u32, "{:4.1}", " 0"; check_fmt_32, 0_u32, "{:04.1}", "0000"; } #[test] fn u256_comp() { let small = U256::from_array([0, 0, 0, 10]); let big = U256::from_array([0, 0, 0x0209_E737_8231_E632, 0x8C8C_3EE7_0C64_4118]); let bigger = U256::from_array([0, 0, 0x0209_E737_8231_E632, 0x9C8C_3EE7_0C64_4118]); let biggest = U256::from_array([1, 0, 0x0209_E737_8231_E632, 0x5C8C_3EE7_0C64_4118]); assert!(small < big); assert!(big < bigger); assert!(bigger < biggest); assert!(bigger <= biggest); assert!(biggest <= biggest); assert!(bigger >= big); assert!(bigger >= small); assert!(small <= small); } const WANT: U256 = U256(0x1bad_cafe_dead_beef_deaf_babe_2bed_feed, 0xbaad_f00d_defa_ceda_11fe_d2ba_d1c0_ffe0); #[rustfmt::skip] const BE_BYTES: [u8; 32] = [ 0x1b, 0xad, 0xca, 0xfe, 0xde, 0xad, 0xbe, 0xef, 0xde, 0xaf, 0xba, 0xbe, 0x2b, 0xed, 0xfe, 0xed, 0xba, 0xad, 0xf0, 0x0d, 0xde, 0xfa, 0xce, 0xda, 0x11, 0xfe, 0xd2, 0xba, 0xd1, 0xc0, 0xff, 0xe0, ]; #[rustfmt::skip] const LE_BYTES: [u8; 32] = [ 0xe0, 0xff, 0xc0, 0xd1, 0xba, 0xd2, 0xfe, 0x11, 0xda, 0xce, 0xfa, 0xde, 0x0d, 0xf0, 0xad, 0xba, 0xed, 0xfe, 0xed, 0x2b, 0xbe, 0xba, 0xaf, 0xde, 0xef, 0xbe, 0xad, 0xde, 0xfe, 0xca, 0xad, 0x1b, ]; // Sanity check that we have the bytes in the correct big-endian order. #[test] fn sanity_be_bytes() { let mut out = [0_u8; 32]; out[..16].copy_from_slice(&WANT.0.to_be_bytes()); out[16..].copy_from_slice(&WANT.1.to_be_bytes()); assert_eq!(out, BE_BYTES); } // Sanity check that we have the bytes in the correct little-endian order. #[test] fn sanity_le_bytes() { let mut out = [0_u8; 32]; out[..16].copy_from_slice(&WANT.1.to_le_bytes()); out[16..].copy_from_slice(&WANT.0.to_le_bytes()); assert_eq!(out, LE_BYTES); } #[test] fn u256_to_be_bytes() { assert_eq!(WANT.to_be_bytes(), BE_BYTES); } #[test] fn u256_from_be_bytes() { assert_eq!(U256::from_be_bytes(BE_BYTES), WANT); } #[test] fn u256_to_le_bytes() { assert_eq!(WANT.to_le_bytes(), LE_BYTES); } #[test] fn u256_from_le_bytes() { assert_eq!(U256::from_le_bytes(LE_BYTES), WANT); } #[test] fn u256_from_u8() { let u = U256::from(0xbe_u8); assert_eq!(u, U256(0, 0xbe)); } #[test] fn u256_from_u16() { let u = U256::from(0xbeef_u16); assert_eq!(u, U256(0, 0xbeef)); } #[test] fn u256_from_u32() { let u = U256::from(0xdeadbeef_u32); assert_eq!(u, U256(0, 0xdeadbeef)); } #[test] fn u256_from_u64() { let u = U256::from(0xdead_beef_cafe_babe_u64); assert_eq!(u, U256(0, 0xdead_beef_cafe_babe)); } #[test] fn u256_from_u128() { let u = U256::from(0xdead_beef_cafe_babe_0123_4567_89ab_cdefu128); assert_eq!(u, U256(0, 0xdead_beef_cafe_babe_0123_4567_89ab_cdef)); } macro_rules! test_from_unsigned_integer_type { ($($test_name:ident, $ty:ident);* $(;)?) => { $( #[test] fn $test_name() { // Internal representation is big-endian. let want = U256(0, 0xAB); let x = 0xAB as $ty; let got = U256::from(x); assert_eq!(got, want); } )* } } test_from_unsigned_integer_type! { from_unsigned_integer_type_u8, u8; from_unsigned_integer_type_u16, u16; from_unsigned_integer_type_u32, u32; from_unsigned_integer_type_u64, u64; from_unsigned_integer_type_u128, u128; } #[test] fn u256_from_be_array_u64() { let array = [ 0x1bad_cafe_dead_beef, 0xdeaf_babe_2bed_feed, 0xbaad_f00d_defa_ceda, 0x11fe_d2ba_d1c0_ffe0, ]; let uint = U256::from_array(array); assert_eq!(uint, WANT); } #[test] fn u256_shift_left() { let u = U256::from(1_u32); assert_eq!(u << 0, u); assert_eq!(u << 1, U256::from(2_u64)); assert_eq!(u << 63, U256::from(0x8000_0000_0000_0000_u64)); assert_eq!(u << 64, U256::from_array([0, 0, 0x0000_0000_0000_0001, 0])); assert_eq!(u << 127, U256(0, 0x8000_0000_0000_0000_0000_0000_0000_0000)); assert_eq!(u << 128, U256(1, 0)); let x = U256(0, 0x8000_0000_0000_0000_0000_0000_0000_0000); assert_eq!(x << 1, U256(1, 0)); } #[test] fn u256_shift_right() { let u = U256(1, 0); assert_eq!(u >> 0, u); assert_eq!(u >> 1, U256(0, 0x8000_0000_0000_0000_0000_0000_0000_0000)); assert_eq!(u >> 127, U256(0, 2)); assert_eq!(u >> 128, U256(0, 1)); } #[test] fn u256_arithmetic() { let init = U256::from(0xDEAD_BEEF_DEAD_BEEF_u64); let copy = init; let add = init.wrapping_add(copy); assert_eq!(add, U256::from_array([0, 0, 1, 0xBD5B_7DDF_BD5B_7DDE])); // Bitshifts let shl = add << 88; assert_eq!(shl, U256::from_array([0, 0x01BD_5B7D, 0xDFBD_5B7D_DE00_0000, 0])); let shr = shl >> 40; assert_eq!(shr, U256::from_array([0, 0, 0x0001_BD5B_7DDF_BD5B, 0x7DDE_0000_0000_0000])); // Increment let mut incr = shr; incr = incr.wrapping_inc(); assert_eq!(incr, U256::from_array([0, 0, 0x0001_BD5B_7DDF_BD5B, 0x7DDE_0000_0000_0001])); // Subtraction let sub = incr.wrapping_sub(init); assert_eq!(sub, U256::from_array([0, 0, 0x0001_BD5B_7DDF_BD5A, 0x9F30_4110_2152_4112])); // Multiplication let (mult, _) = sub.mul_u64(300); assert_eq!(mult, U256::from_array([0, 0, 0x0209_E737_8231_E632, 0x8C8C_3EE7_0C64_4118])); // Division assert_eq!(U256::from(105_u32) / U256::from(5_u32), U256::from(21_u32)); let div = mult / U256::from(300_u32); assert_eq!(div, U256::from_array([0, 0, 0x0001_BD5B_7DDF_BD5A, 0x9F30_4110_2152_4112])); assert_eq!(U256::from(105_u32) % U256::from(5_u32), U256::ZERO); assert_eq!(U256::from(35498456_u32) % U256::from(3435_u32), U256::from(1166_u32)); let rem_src = mult.wrapping_mul(U256::from(39842_u32)).wrapping_add(U256::from(9054_u32)); assert_eq!(rem_src % U256::from(39842_u32), U256::from(9054_u32)); } #[test] fn u256_bit_inversion() { let v = U256(1, 0); let want = U256( 0xffff_ffff_ffff_ffff_ffff_ffff_ffff_fffe, 0xffff_ffff_ffff_ffff_ffff_ffff_ffff_ffff, ); assert_eq!(!v, want); let v = U256(0x0c0c_0c0c_0c0c_0c0c_0c0c_0c0c_0c0c_0c0c, 0xeeee_eeee_eeee_eeee); let want = U256( 0xf3f3_f3f3_f3f3_f3f3_f3f3_f3f3_f3f3_f3f3, 0xffff_ffff_ffff_ffff_1111_1111_1111_1111, ); assert_eq!(!v, want); } #[test] fn u256_mul_u64_by_one() { let v = U256::from(0xDEAD_BEEF_DEAD_BEEF_u64); assert_eq!(v, v.mul_u64(1_u64).0); } #[test] fn u256_mul_u64_by_zero() { let v = U256::from(0xDEAD_BEEF_DEAD_BEEF_u64); assert_eq!(U256::ZERO, v.mul_u64(0_u64).0); } #[test] fn u256_mul_u64() { let u64_val = U256::from(0xDEAD_BEEF_DEAD_BEEF_u64); let u96_res = u64_val.mul_u64(0xFFFF_FFFF).0; let u128_res = u96_res.mul_u64(0xFFFF_FFFF).0; let u160_res = u128_res.mul_u64(0xFFFF_FFFF).0; let u192_res = u160_res.mul_u64(0xFFFF_FFFF).0; let u224_res = u192_res.mul_u64(0xFFFF_FFFF).0; let u256_res = u224_res.mul_u64(0xFFFF_FFFF).0; assert_eq!(u96_res, U256::from_array([0, 0, 0xDEAD_BEEE, 0xFFFF_FFFF_2152_4111])); assert_eq!( u128_res, U256::from_array([0, 0, 0xDEAD_BEEE_2152_4110, 0x2152_4111_DEAD_BEEF]) ); assert_eq!( u160_res, U256::from_array([0, 0xDEAD_BEED, 0x42A4_8222_0000_0001, 0xBD5B_7DDD_2152_4111]) ); assert_eq!( u192_res, U256::from_array([ 0, 0xDEAD_BEEC_63F6_C334, 0xBD5B_7DDF_BD5B_7DDB, 0x63F6_C333_DEAD_BEEF ]) ); assert_eq!( u224_res, U256::from_array([ 0xDEAD_BEEB, 0x8549_0448_5964_BAAA, 0xFFFF_FFFB_A69B_4558, 0x7AB6_FBBB_2152_4111 ]) ); assert_eq!( u256_res, U256( 0xDEAD_BEEA_A69B_455C_D41B_B662_A69B_4550, 0xA69B_455C_D41B_B662_A69B_4555_DEAD_BEEF, ) ); } #[test] fn u256_addition() { let x = U256::from(u128::MAX); let (add, overflow) = x.overflowing_add(U256::ONE); assert!(!overflow); assert_eq!(add, U256(1, 0)); let (add, _) = add.overflowing_add(U256::ONE); assert_eq!(add, U256(1, 1)); } #[test] fn u256_subtraction() { let (sub, overflow) = U256::ONE.overflowing_sub(U256::ONE); assert!(!overflow); assert_eq!(sub, U256::ZERO); let x = U256(1, 0); let (sub, overflow) = x.overflowing_sub(U256::ONE); assert!(!overflow); assert_eq!(sub, U256::from(u128::MAX)); } #[test] fn u256_multiplication() { let u64_val = U256::from(0xDEAD_BEEF_DEAD_BEEF_u64); let u128_res = u64_val.wrapping_mul(u64_val); assert_eq!(u128_res, U256(0, 0xC1B1_CD13_A4D1_3D46_048D_1354_216D_A321)); let u256_res = u128_res.wrapping_mul(u128_res); assert_eq!( u256_res, U256( 0x928D_92B4_D7F5_DF33_4AFC_FF6F_0375_C608, 0xF5CF_7F36_18C2_C886_F4E1_66AA_D40D_0A41, ) ); } #[test] fn u256_multiplication_bits_in_each_word() { // Put a digit in the least significant bit of each 64 bit word. let u = 1_u128 << 64 | 1_u128; let x = U256(u, u); // Put a digit in the second least significant bit of each 64 bit word. let u = 2_u128 << 64 | 2_u128; let y = U256(u, u); let (got, overflow) = x.overflowing_mul(y); let want = U256( 0x0000_0000_0000_0008_0000_0000_0000_0008, 0x0000_0000_0000_0006_0000_0000_0000_0004, ); assert!(!overflow); assert_eq!(got, want) } #[test] fn u256_increment() { let mut val = U256( 0xEFFF_FFFF_FFFF_FFFF_FFFF_FFFF_FFFF_FFFF, 0xFFFF_FFFF_FFFF_FFFF_FFFF_FFFF_FFFF_FFFE, ); val = val.wrapping_inc(); assert_eq!( val, U256( 0xEFFF_FFFF_FFFF_FFFF_FFFF_FFFF_FFFF_FFFF, 0xFFFF_FFFF_FFFF_FFFF_FFFF_FFFF_FFFF_FFFF, ) ); val = val.wrapping_inc(); assert_eq!( val, U256( 0xF000_0000_0000_0000_0000_0000_0000_0000, 0x0000_0000_0000_0000_0000_0000_0000_0000, ) ); assert_eq!(U256::MAX.wrapping_inc(), U256::ZERO); } #[test] fn u256_extreme_bitshift() { // Shifting a u64 by 64 bits gives an undefined value, so make sure that // we're doing the Right Thing here let init = U256::from(0xDEAD_BEEF_DEAD_BEEF_u64); assert_eq!(init << 64, U256(0, 0xDEAD_BEEF_DEAD_BEEF_0000_0000_0000_0000)); let add = (init << 64).wrapping_add(init); assert_eq!(add, U256(0, 0xDEAD_BEEF_DEAD_BEEF_DEAD_BEEF_DEAD_BEEF)); assert_eq!(add >> 0, U256(0, 0xDEAD_BEEF_DEAD_BEEF_DEAD_BEEF_DEAD_BEEF)); assert_eq!(add << 0, U256(0, 0xDEAD_BEEF_DEAD_BEEF_DEAD_BEEF_DEAD_BEEF)); assert_eq!(add >> 64, U256(0, 0x0000_0000_0000_0000_DEAD_BEEF_DEAD_BEEF)); assert_eq!( add << 64, U256(0xDEAD_BEEF_DEAD_BEEF, 0xDEAD_BEEF_DEAD_BEEF_0000_0000_0000_0000) ); } #[cfg(feature = "serde")] #[test] fn u256_serde() { let check = |uint, hex| { let json = format!("\"{}\"", hex); assert_eq!(::serde_json::to_string(&uint).unwrap(), json); assert_eq!(::serde_json::from_str::(&json).unwrap(), uint); let bin_encoded = bincode::serialize(&uint).unwrap(); let bin_decoded: U256 = bincode::deserialize(&bin_encoded).unwrap(); assert_eq!(bin_decoded, uint); }; check(U256::ZERO, "0000000000000000000000000000000000000000000000000000000000000000"); check( U256::from(0xDEADBEEF_u32), "00000000000000000000000000000000000000000000000000000000deadbeef", ); check( U256::from_array([0xdd44, 0xcc33, 0xbb22, 0xaa11]), "000000000000dd44000000000000cc33000000000000bb22000000000000aa11", ); check(U256::MAX, "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"); check( U256( 0xDEAD_BEEA_A69B_455C_D41B_B662_A69B_4550, 0xA69B_455C_D41B_B662_A69B_4555_DEAD_BEEF, ), "deadbeeaa69b455cd41bb662a69b4550a69b455cd41bb662a69b4555deadbeef", ); assert!(::serde_json::from_str::( "\"fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffg\"" ) .is_err()); // invalid char assert!(::serde_json::from_str::( "\"ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff\"" ) .is_err()); // invalid length assert!(::serde_json::from_str::( "\"ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff\"" ) .is_err()); // invalid length } #[test] fn u256_is_max_correct_negative() { let tc = vec![U256::ZERO, U256::ONE, U256::from(u128::MAX)]; for t in tc { assert!(!t.is_max()) } } #[test] fn u256_is_max_correct_positive() { assert!(U256::MAX.is_max()); let u = u128::MAX; assert!(((U256::from(u) << 128) + U256::from(u)).is_max()); } #[test] fn compact_target_from_hex_lower() { let target = CompactTarget::from_hex("0x010034ab").unwrap(); assert_eq!(target, CompactTarget(0x010034ab)); } #[test] fn compact_target_from_hex_upper() { let target = CompactTarget::from_hex("0X010034AB").unwrap(); assert_eq!(target, CompactTarget(0x010034ab)); } #[test] fn compact_target_from_unprefixed_hex_lower() { let target = CompactTarget::from_unprefixed_hex("010034ab").unwrap(); assert_eq!(target, CompactTarget(0x010034ab)); } #[test] fn compact_target_from_unprefixed_hex_upper() { let target = CompactTarget::from_unprefixed_hex("010034AB").unwrap(); assert_eq!(target, CompactTarget(0x010034ab)); } #[test] fn compact_target_from_hex_invalid_hex_should_err() { let hex = "0xzbf9"; let result = CompactTarget::from_hex(hex); assert!(result.is_err()); } #[test] fn compact_target_lower_hex_and_upper_hex() { assert_eq!(format!("{:08x}", CompactTarget(0x01D0F456)), "01d0f456"); assert_eq!(format!("{:08X}", CompactTarget(0x01d0f456)), "01D0F456"); } #[test] fn target_from_compact() { // (nBits, target) let tests = vec![ (0x0100_3456_u32, 0x00_u64), // High bit set. (0x0112_3456_u32, 0x12_u64), (0x0200_8000_u32, 0x80_u64), (0x0500_9234_u32, 0x9234_0000_u64), (0x0492_3456_u32, 0x00_u64), // High bit set (0x80 in 0x92). (0x0412_3456_u32, 0x1234_5600_u64), // Inverse of above; no high bit. ]; for (n_bits, target) in tests { let want = Target::from(target); let got = Target::from_compact(CompactTarget::from_consensus(n_bits)); assert_eq!(got, want); } } #[test] fn target_is_met_by_for_target_equals_hash() { use std::str::FromStr; use hashes::Hash; let hash = BlockHash::from_str("ef537f25c895bfa782526529a9b63d97aa631564d5d789c2b765448c8635fb6c") .expect("failed to parse block hash"); let target = Target(U256::from_le_bytes(hash.to_byte_array())); assert!(target.is_met_by(hash)); } #[test] fn max_target_from_compact() { // The highest possible target is defined as 0x1d00ffff let bits = 0x1d00ffff_u32; let want = Target::MAX; let got = Target::from_compact(CompactTarget::from_consensus(bits)); assert_eq!(got, want) } #[test] fn target_difficulty_float() { assert_eq!(Target::MAX.difficulty_float(), 1.0_f64); assert_eq!( Target::from_compact(CompactTarget::from_consensus(0x1c00ffff_u32)).difficulty_float(), 256.0_f64 ); assert_eq!( Target::from_compact(CompactTarget::from_consensus(0x1b00ffff_u32)).difficulty_float(), 65536.0_f64 ); assert_eq!( Target::from_compact(CompactTarget::from_consensus(0x1a00f3a2_u32)).difficulty_float(), 17628585.065897066_f64 ); } #[test] fn roundtrip_compact_target() { let consensus = 0x1d00_ffff; let compact = CompactTarget::from_consensus(consensus); let t = Target::from_compact(CompactTarget::from_consensus(consensus)); assert_eq!(t, Target::from(compact)); // From/Into sanity check. let back = t.to_compact_lossy(); assert_eq!(back, compact); // From/Into sanity check. assert_eq!(back.to_consensus(), consensus); } #[test] fn roundtrip_target_work() { let target = Target::from(0xdeadbeef_u32); let work = target.to_work(); let back = work.to_target(); assert_eq!(back, target) } #[cfg(feature = "std")] #[test] fn work_log2() { // Compare work log2 to historical Bitcoin Core values found in Core logs. let tests: Vec<(u128, f64)> = vec![ // (chainwork, core log2) // height (0x200020002, 33.000022), // 1 (0xa97d67041c5e51596ee7, 79.405055), // 308004 (0x1dc45d79394baa8ab18b20, 84.895644), // 418141 (0x8c85acb73287e335d525b98, 91.134654), // 596624 (0x2ef447e01d1642c40a184ada, 93.553183), // 738965 ]; for (chainwork, core_log2) in tests { // Core log2 in the logs is rounded to 6 decimal places. let log2 = (Work::from(chainwork).log2() * 1e6).round() / 1e6; assert_eq!(log2, core_log2) } assert_eq!(Work(U256::ONE).log2(), 0.0); assert_eq!(Work(U256::MAX).log2(), 256.0); } #[test] fn u256_zero_min_max_inverse() { assert_eq!(U256::MAX.inverse(), U256::ONE); assert_eq!(U256::ONE.inverse(), U256::MAX); assert_eq!(U256::ZERO.inverse(), U256::MAX); } #[test] fn u256_max_min_inverse_roundtrip() { let max = U256::MAX; for min in [U256::ZERO, U256::ONE].iter() { // lower target means more work required. assert_eq!(Target(max).to_work(), Work(U256::ONE)); assert_eq!(Target(*min).to_work(), Work(max)); assert_eq!(Work(max).to_target(), Target(U256::ONE)); assert_eq!(Work(*min).to_target(), Target(max)); } } #[test] fn u256_wrapping_add_wraps_at_boundary() { assert_eq!(U256::MAX.wrapping_add(U256::ONE), U256::ZERO); assert_eq!(U256::MAX.wrapping_add(U256::from(2_u8)), U256::ONE); } #[test] fn u256_wrapping_sub_wraps_at_boundary() { assert_eq!(U256::ZERO.wrapping_sub(U256::ONE), U256::MAX); assert_eq!(U256::ONE.wrapping_sub(U256::from(2_u8)), U256::MAX); } #[test] fn mul_u64_overflows() { let (_, overflow) = U256::MAX.mul_u64(2); assert!(overflow, "max * 2 should overflow"); } #[test] #[cfg(debug_assertions)] #[should_panic] fn u256_overflowing_addition_panics() { let _ = U256::MAX + U256::ONE; } #[test] #[cfg(debug_assertions)] #[should_panic] fn u256_overflowing_subtraction_panics() { let _ = U256::ZERO - U256::ONE; } #[test] #[cfg(debug_assertions)] #[should_panic] fn u256_multiplication_by_max_panics() { let _ = U256::MAX * U256::MAX; } #[test] #[cfg(debug_assertions)] #[should_panic] fn work_overflowing_addition_panics() { let _ = Work(U256::MAX) + Work(U256::ONE); } #[test] #[cfg(debug_assertions)] #[should_panic] fn work_overflowing_subtraction_panics() { let _ = Work(U256::ZERO) - Work(U256::ONE); } #[test] fn u256_to_f64() { // Validate that the Target::MAX value matches the constant also used in difficulty calculation. assert_eq!(Target::MAX.0.to_f64(), TARGET_MAX_F64); assert_eq!(U256::ZERO.to_f64(), 0.0_f64); assert_eq!(U256::ONE.to_f64(), 1.0_f64); assert_eq!(U256::MAX.to_f64(), 1.157920892373162e77_f64); assert_eq!((U256::MAX >> 1).to_f64(), 5.78960446186581e76_f64); assert_eq!((U256::MAX >> 128).to_f64(), 3.402823669209385e38_f64); assert_eq!((U256::MAX >> (256 - 54)).to_f64(), 1.8014398509481984e16_f64); // 53 bits and below should not use exponents assert_eq!((U256::MAX >> (256 - 53)).to_f64(), 9007199254740991.0_f64); assert_eq!((U256::MAX >> (256 - 32)).to_f64(), 4294967295.0_f64); assert_eq!((U256::MAX >> (256 - 16)).to_f64(), 65535.0_f64); assert_eq!((U256::MAX >> (256 - 8)).to_f64(), 255.0_f64); } } #[cfg(kani)] mod verification { use super::*; #[kani::unwind(5)] // mul_u64 loops over 4 64 bit ints so use one more than 4 #[kani::proof] fn check_mul_u64() { let x: U256 = kani::any(); let y: u64 = kani::any(); let _ = x.mul_u64(y); } }