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use crate::Uint;
impl<const BITS: usize, const LIMBS: usize> Uint<BITS, LIMBS> {
/// Raises self to the power of `exp`.
///
/// Returns None if the result would overflow.
#[inline]
#[must_use]
pub fn checked_pow(self, exp: Self) -> Option<Self> {
match self.overflowing_pow(exp) {
(x, false) => Some(x),
(_, true) => None,
}
}
/// Raises self to the power of `exp` and if the result would overflow.
///
/// # Examples
///
/// ```
/// # use ruint::{Uint, uint};
/// # uint!{
/// assert_eq!(
/// 36_U64.overflowing_pow(12_U64),
/// (0x41c21cb8e1000000_U64, false)
/// );
/// assert_eq!(
/// 36_U64.overflowing_pow(13_U64),
/// (0x3f4c09ffa4000000_U64, true)
/// );
/// assert_eq!(
/// 36_U68.overflowing_pow(13_U68),
/// (0x093f4c09ffa4000000_U68, false)
/// );
/// assert_eq!(16_U65.overflowing_pow(32_U65), (0_U65, true));
/// # }
/// ```
/// Small cases:
/// ```
/// # use ruint::{Uint, uint};
/// # uint!{
/// assert_eq!(0_U0.overflowing_pow(0_U0), (0_U0, false));
/// assert_eq!(0_U1.overflowing_pow(0_U1), (1_U1, false));
/// assert_eq!(0_U1.overflowing_pow(1_U1), (0_U1, false));
/// assert_eq!(1_U1.overflowing_pow(0_U1), (1_U1, false));
/// assert_eq!(1_U1.overflowing_pow(1_U1), (1_U1, false));
/// # }
/// ```
#[inline]
#[must_use]
pub fn overflowing_pow(mut self, mut exp: Self) -> (Self, bool) {
if BITS == 0 {
return (self, false);
}
// Exponentiation by squaring
let mut overflow = false;
let mut base_overflow = false;
let mut result = Self::ONE;
while !exp.is_zero() {
// Multiply by base
if exp.bit(0) {
let (r, o) = result.overflowing_mul(self);
result = r;
overflow |= o | base_overflow;
}
// Square base
let (s, o) = self.overflowing_mul(self);
self = s;
base_overflow |= o;
exp >>= 1;
}
(result, overflow)
}
/// Raises self to the power of `exp`, wrapping around on overflow.
#[inline]
#[must_use]
pub fn pow(self, exp: Self) -> Self {
self.wrapping_pow(exp)
}
/// Raises self to the power of `exp`, saturating on overflow.
#[inline]
#[must_use]
pub fn saturating_pow(self, exp: Self) -> Self {
match self.overflowing_pow(exp) {
(x, false) => x,
(_, true) => Self::MAX,
}
}
/// Raises self to the power of `exp`, wrapping around on overflow.
#[inline]
#[must_use]
pub fn wrapping_pow(mut self, mut exp: Self) -> Self {
if BITS == 0 {
return self;
}
// Exponentiation by squaring
let mut result = Self::ONE;
while !exp.is_zero() {
// Multiply by base
if exp.bit(0) {
result = result.wrapping_mul(self);
}
// Square base
self = self.wrapping_mul(self);
exp >>= 1;
}
result
}
/// Construct from double precision binary logarithm.
///
/// # Examples
///
/// ```
/// # use ruint::{Uint, uint, aliases::*};
/// # uint!{
/// assert_eq!(U64::approx_pow2(-2.0), Some(0_U64));
/// assert_eq!(U64::approx_pow2(-1.0), Some(1_U64));
/// assert_eq!(U64::approx_pow2(0.0), Some(1_U64));
/// assert_eq!(U64::approx_pow2(1.0), Some(2_U64));
/// assert_eq!(U64::approx_pow2(1.6), Some(3_U64));
/// assert_eq!(U64::approx_pow2(2.0), Some(4_U64));
/// assert_eq!(U64::approx_pow2(64.0), None);
/// assert_eq!(U64::approx_pow2(10.385), Some(1337_U64));
/// # }
/// ```
#[cfg(feature = "std")]
#[must_use]
#[allow(clippy::missing_inline_in_public_items)]
pub fn approx_pow2(exp: f64) -> Option<Self> {
const LN2_1P5: f64 = 0.584_962_500_721_156_2_f64;
const EXP2_63: f64 = 9_223_372_036_854_775_808_f64;
// FEATURE: Round negative to zero.
#[allow(clippy::cast_precision_loss)] // Self::BITS ~< 2^52 and so fits f64.
if exp < LN2_1P5 {
if exp < -1.0 {
return Some(Self::ZERO);
}
return Self::try_from(1).ok();
}
#[allow(clippy::cast_precision_loss)]
if exp > Self::BITS as f64 {
return None;
}
// Since exp < BITS, it has an integer and fractional part.
#[allow(clippy::cast_possible_truncation)] // exp <= BITS <= usize::MAX.
#[allow(clippy::cast_sign_loss)] // exp >= 0.
let shift = exp.trunc() as usize;
let fract = exp.fract();
// Compute the leading 64 bits
// Since `fract < 1.0` we have `fract.exp2() < 2`, so we can rescale by
// 2^63 and cast to u64.
#[allow(clippy::cast_possible_truncation)] // fract < 1.0
#[allow(clippy::cast_sign_loss)] // fract >= 0.
let bits = (fract.exp2() * EXP2_63) as u64;
// Note: If `fract` is zero this will result in `u64::MAX`.
if shift >= 63 {
// OPT: A dedicated function avoiding full-sized shift.
Some(Self::try_from(bits).ok()?.checked_shl(shift - 63)?)
} else {
let shift = 63 - shift;
// Divide `bits` by `2^shift`, rounding to nearest.
let bits = (bits >> shift) + ((bits >> (shift - 1)) & 1);
Self::try_from(bits).ok()
}
}
}
#[cfg(test)]
mod tests {
use super::*;
use crate::{const_for, nlimbs};
use core::iter::repeat_n;
use proptest::proptest;
#[test]
fn test_pow2_shl() {
const_for!(BITS in NON_ZERO if BITS >= 2 {
const LIMBS: usize = nlimbs(BITS);
type U = Uint<BITS, LIMBS>;
proptest!(|(e in 0..=BITS+1)| {
assert_eq!(U::from(2).pow(U::from(e)), U::from(1) << e);
});
});
}
#[test]
fn test_pow_product() {
const_for!(BITS in NON_ZERO if BITS >= 64 {
const LIMBS: usize = nlimbs(BITS);
type U = Uint<BITS, LIMBS>;
proptest!(|(b in 2_u64..100, e in 0_usize..100)| {
let b = U::from(b);
let prod = repeat_n(b, e).product::<U>();
assert_eq!(b.pow(U::from(e)), prod);
});
});
}
}