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#![cfg(feature = "std")]
use crate::Uint;
impl<const BITS: usize, const LIMBS: usize> Uint<BITS, LIMBS> {
/// Returns the logarithm of the number, rounded down.
///
/// Returns None if the base is less than two, or this number is zero.
#[inline]
#[must_use]
pub fn checked_log(self, base: Self) -> Option<usize> {
if base < Self::from(2) || self.is_zero() {
return None;
}
Some(self.log(base))
}
/// Returns the base 10 logarithm of the number, rounded down.
///
/// Returns None if the number is zero.
#[inline]
#[must_use]
pub fn checked_log10(self) -> Option<usize> {
self.checked_log(Self::from(10))
}
/// Returns the base 2 logarithm of the number, rounded down.
///
/// This is equivalent to the index of the highest set bit.
///
/// Returns None if the number is zero.
#[inline]
#[must_use]
pub fn checked_log2(self) -> Option<usize> {
self.checked_log(Self::from(2))
}
/// Returns the logarithm of the number, rounded down.
///
/// # Panics
///
/// Panics if the `base` is less than 2 or if the number is zero.
#[inline]
#[must_use]
pub fn log(self, base: Self) -> usize {
assert!(!self.is_zero());
assert!(base >= Self::from(2));
if base == Self::from(2) {
return self.bit_len() - 1;
}
if self < base {
return 0;
}
// Find approximate result
#[allow(clippy::cast_precision_loss)] // Casting base to `f64` is fine.
let result = self.approx_log2() / base.approx_log2();
// We handled edge cases above, so the result should be normal and fit `Self`.
assert!(result.is_normal());
let mut result = result.try_into().unwrap();
// Adjust result to get the exact value. At most one of these should happen, but
// we loop regardless.
loop {
if let Some(value) = base.checked_pow(result) {
if value > self {
assert!(!result.is_zero());
result -= Self::ONE;
continue;
}
} else {
// Overflow, so definitely larger than `value`
result -= Self::ONE;
}
break;
}
while let Some(trial) = result.checked_add(Self::ONE) {
if let Some(value) = base.checked_pow(trial) {
if value <= self {
result = trial;
continue;
}
}
break;
}
// Should always be possible.
result.to()
}
/// Returns the base 10 logarithm of the number, rounded down.
///
/// # Panics
///
/// Panics if the `base` if the number is zero.
#[inline]
#[must_use]
pub fn log10(self) -> usize {
self.log(Self::from(10))
}
/// Returns the base 2 logarithm of the number, rounded down.
///
/// # Panics
///
/// Panics if the `base` if the number is zero.
#[inline]
#[must_use]
pub fn log2(self) -> usize {
self.log(Self::from(2))
}
/// Double precision logarithm.
#[inline]
#[must_use]
pub fn approx_log(self, base: f64) -> f64 {
self.approx_log2() / base.log2()
}
/// Double precision binary logarithm.
///
/// # Examples
///
/// ```
/// # use ruint::{Uint, uint, aliases::*};
/// # uint!{
/// assert_eq!(0_U64.approx_log2(), f64::NEG_INFINITY);
/// assert_eq!(1_U64.approx_log2(), 0.0);
/// assert_eq!(2_U64.approx_log2(), 1.0);
/// assert_eq!(U64::MAX.approx_log2(), 64.0);
/// # }
/// ```
#[inline]
#[must_use]
#[allow(clippy::cast_precision_loss)]
pub fn approx_log2(self) -> f64 {
// The naive solution would be `f64::from(self).log2()`, but
// `f64::from(self)` quickly overflows (`f64::MAX` is 2^1024).
// So instead we first approximate as `bits * 2^exp` and then
// compute using`log2(bits * 2^exp) = log2(bits) + exp`
let (bits, exp) = self.most_significant_bits();
// Convert to floats
let bits = bits as f64;
let exp = exp as f64;
bits.log2() + exp
}
/// Double precision decimal logarithm.
#[inline]
#[must_use]
pub fn approx_log10(self) -> f64 {
self.approx_log2() / core::f64::consts::LOG2_10
}
}
#[cfg(test)]
mod tests {
use super::*;
use crate::{aliases::U128, const_for, nlimbs};
use proptest::{prop_assume, proptest};
#[test]
fn test_checked_log2() {
assert_eq!(U128::from(0).checked_log2(), None);
assert_eq!(U128::from(1).checked_log2(), Some(0));
assert_eq!(U128::from(2).checked_log2(), Some(1));
assert_eq!(U128::from(3).checked_log2(), Some(1));
assert_eq!(U128::from(127).checked_log2(), Some(6));
assert_eq!(U128::from(128).checked_log2(), Some(7));
}
#[test]
fn test_approx_log2_pow2() {
const_for!(BITS in SIZES {
const LIMBS: usize = nlimbs(BITS);
type U = Uint<BITS, LIMBS>;
proptest!(|(value: U)| {
let log = value.approx_log2();
let pow = U::approx_pow2(log).unwrap();
let error = value.abs_diff(pow);
let correct_bits = value.bit_len() - error.bit_len();
// The maximum precision we could expect here is 53 bits.
// OPT: Find out exactly where the precision is lost and what
// the bounds are.
assert!(correct_bits == value.bit_len() || correct_bits >= 42);
});
});
}
#[test]
fn test_pow_log() {
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..BITS)| {
if let Some(value) = U::from(b).checked_pow(U::from(e)) {
assert!(value > U::ZERO);
assert_eq!(value.log(U::from(b)), e);
// assert_eq!(value.log(b + U::ONE), e as u64);
}
});
});
}
#[test]
fn test_log_pow() {
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, n: U)| {
prop_assume!(n > U::ZERO);
let e = n.log(U::from(b));
assert!(U::from(b).pow(U::from(e)) <= n);
if let Some(value) = U::from(b).checked_pow(U::from(e + 1)) {
assert!(value > n);
}
});
});
}
}