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Optimize from/assign str for power of 2 bases #78

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Feb 8, 2025
Merged

Optimize from/assign str for power of 2 bases #78

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eab7897
Optimize from/assign str for binary bases
OTheDev Feb 8, 2025
aa02240
Clean up mult
OTheDev Feb 8, 2025
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50 changes: 50 additions & 0 deletions arbi/scripts/size_in_radix.py
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Original file line number Diff line number Diff line change
@@ -0,0 +1,50 @@
###############################################################################
# Copyright 2025 Owain Davies
# SPDX-License-Identifier: Apache-2.0 OR MIT
#
# This file is part of "arbi", an Arbitrary Precision Integer library for Rust.
###############################################################################

from decimal import getcontext, Decimal, ROUND_CEILING

# Some high enough precision :)
getcontext().prec = 100


# ceil( (log(2) / log(base)) * 2^(digit_bits) )
# Useful for computing the needed capacity for Arbi::to_string()-type functions
def log2_div_logb(base: int, digit_bits: int = 32) -> int:
x = Decimal(2).ln() / Decimal(base).ln()
scaled = x * Decimal(1 << digit_bits)

return int(scaled.to_integral_exact(ROUND_CEILING))


# ceil( (log(base) / log(2^(digit_bits))) * 2^(digit_bits) )
# Useful for computing the needed capacity for Arbi::from_str()-type functions
def logb_div_logab(base: int, digit_bits: int = 32) -> int:
x = Decimal(base).ln() / Decimal(1 << digit_bits).ln()
scaled = x * Decimal(1 << digit_bits)

return int(scaled.to_integral_exact(ROUND_CEILING))


def print_arrays():
def print_array(prefix: str, digit_bits: int, func, start_base: int):
print(f"const {prefix}_{digit_bits}: [u{digit_bits}; 37] = [")

max_hex_digits = digit_bits >> 2
for base in range(start_base): # Use 0 for bases [0, start_base)
print(f"{' ' * 4}0x{'0' * max_hex_digits},")
for base in range(start_base, 37):
print(f"{' ' * 4}0x{func(base, digit_bits):x},")

print("];\n")

for digit_bits in (32, 64):
print_array("SCALED_LOG2_DIV_LOG", digit_bits, log2_div_logb, 3)
print_array("SCALED_LOGB_DIV_LOGAB", digit_bits, logb_div_logab, 2)


if __name__ == "__main__":
print_arrays()
101 changes: 81 additions & 20 deletions arbi/src/assign_string.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -4,9 +4,7 @@ SPDX-License-Identifier: Apache-2.0 OR MIT
*/

use crate::from_string::{configs::BASE_MBS, BaseMbs, ParseError};
use crate::uints::UnsignedUtilities;
use crate::Base;
use crate::{Arbi, Digit};
use crate::{Arbi, Base, Digit};

impl Arbi {
/// Assign the integer value the provided string represents to this `Arbi`
Expand Down Expand Up @@ -137,20 +135,85 @@ impl Arbi {
return Ok(());
}

// Get configuration for this base
let base_val = base.value() as u32;
let BaseMbs { mbs, base_pow_mbs } = BASE_MBS[base_val as usize];
let base_value = base.value() as u32;

// Reserve estimated capacity
let estimate = usize::div_ceil_(base_digits.len(), mbs);
self.vec
.reserve(estimate.saturating_sub(self.vec.capacity()));
let capacity = Self::size_with_size_base_maybe_over_by_one(
base_value,
base_digits.len(),
);
self.vec.clear();
self.neg = has_minus_sign;
self.vec.reserve(capacity);

#[cfg(debug_assertions)]
let initial_capacity = self.vec.capacity();

self.neg = has_minus_sign;

if base_value.is_power_of_two() {
self.assign_str_radix_algo_pow2(base_digits, base_value)?
} else {
self.assign_str_radix_algo_generic(base_digits, base_value)?
}

#[cfg(debug_assertions)]
{
debug_assert_eq!(self.vec.capacity(), initial_capacity);
debug_assert!(
self.vec.len() == capacity || self.vec.len() == capacity - 1
);
}

Ok(())
}

fn assign_str_radix_algo_pow2(
&mut self,
base_digits: &[u8],
base: u32,
) -> Result<(), ParseError> {
debug_assert!(!base_digits.is_empty());
debug_assert!((2..=36).contains(&base) && base.is_power_of_two());

// Number of bits in a base-`base` digit.
let bits_in_base_digit: u32 = base.trailing_zeros();
let mut shift: u32 = 0;
let mut digit: Digit = 0;
for &c in base_digits.iter().rev() {
let base_digit: Digit = match (c as char).to_digit(base) {
Some(base_digit) => base_digit as Digit,
None => return Err(ParseError::InvalidDigit),
};
digit |= base_digit << shift;
shift += bits_in_base_digit;
if Digit::BITS <= shift {
self.vec.push(digit);
shift -= Digit::BITS;
/*
On Digit::BITS == shift, digit is simply reset to 0.
On Digit::BITS < shift, digit will be set to the remaining
bits in the current base digit that could not fit in the
just pushed Arbi::BASE-digit, so no information is lost.
*/
digit = base_digit >> (bits_in_base_digit - shift);
}
}
if digit != 0 {
self.vec.push(digit);
}

Ok(())
}

/* Generic Algorithm (works for all valid bases) */
fn assign_str_radix_algo_generic(
&mut self,
base_digits: &[u8],
base: u32,
) -> Result<(), ParseError> {
debug_assert!(!base_digits.is_empty());
debug_assert!((2..=36).contains(&base));

let BaseMbs { mbs, base_pow_mbs } = BASE_MBS[base as usize];
let n_base = base_digits.len();
let rem_batch_size = n_base % mbs;
let mut pos = 0;
Expand All @@ -162,9 +225,9 @@ impl Arbi {
// Convert batch substring to integer value
let end = pos + rem_batch_size;
while pos < end {
match (base_digits[pos] as char).to_digit(base_val) {
Some(digit) => {
batch = digit + batch * base_val;
match (base_digits[pos] as char).to_digit(base) {
Some(base_digit) => {
batch = base_digit + batch * base;
pos += 1;
}
None => return Err(ParseError::InvalidDigit),
Expand All @@ -181,9 +244,9 @@ impl Arbi {
// Convert batch substring to integer value
let end = pos + mbs;
while pos < end {
match (base_digits[pos] as char).to_digit(base_val) {
Some(digit) => {
batch = digit + batch * base_val;
match (base_digits[pos] as char).to_digit(base) {
Some(base_digit) => {
batch = base_digit + batch * base;
pos += 1;
}
None => return Err(ParseError::InvalidDigit),
Expand All @@ -192,10 +255,8 @@ impl Arbi {
Self::imul1add1(self, base_pow_mbs, Some(batch));
}

#[cfg(debug_assertions)]
debug_assert_eq!(self.vec.capacity(), initial_capacity);

self.trim();

Ok(())
}

Expand Down
2 changes: 1 addition & 1 deletion arbi/src/multiplication.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -26,7 +26,7 @@ impl Arbi {
///
/// ## Complexity
/// \\( O(n) \\)
#[allow(dead_code)]
#[inline(always)]
pub(crate) fn imul1add1(x: &mut Self, v: Digit, k: Option<Digit>) {
let mut k: Digit = k.unwrap_or(0);
for d in &mut x.vec {
Expand Down
14 changes: 1 addition & 13 deletions arbi/src/size.rs
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Expand Up @@ -16,13 +16,10 @@ impl Arbi {
/// # Examples
/// ```
/// use arbi::{Arbi, Digit};
///
/// let zero = Arbi::zero();
/// assert_eq!(zero.size(), 0);
///
/// let mut a = Arbi::from(Digit::MAX);
/// assert_eq!(a.size(), 1);
///
/// a += 1;
/// assert_eq!(a.size(), 2);
/// ```
Expand All @@ -42,10 +39,8 @@ impl Arbi {
/// # Examples
/// ```
/// use arbi::{Arbi, BitCount, Digit};
///
/// let zero = Arbi::zero();
/// assert_eq!(zero.size_bits(), 0);
///
/// let mut a = Arbi::from(Digit::MAX);
/// assert_eq!(a.size_bits(), Digit::BITS as BitCount);
/// a += 1;
Expand Down Expand Up @@ -106,15 +101,12 @@ impl Arbi {
/// # Examples
/// ```
/// use arbi::Arbi;
///
/// let mut zero = Arbi::zero();
/// assert_eq!(zero.size_base_mut(10), 0);
/// assert_eq!(zero, 0);
///
/// let mut one = Arbi::one();
/// assert_eq!(one.size_base_mut(10), 1);
/// assert_eq!(one, 1);
///
/// let mut a = Arbi::from_str_radix("123456789", 10).unwrap();
/// assert_eq!(a.size_base_mut(10), 9);
/// assert_eq!(a, 9);
Expand Down Expand Up @@ -148,13 +140,10 @@ impl Arbi {
/// # Examples
/// ```
/// use arbi::Arbi;
///
/// let zero = Arbi::zero();
/// assert_eq!(zero.size_base_ref(10), 0);
///
/// let one = Arbi::one();
/// assert_eq!(one.size_base_ref(10), 1);
///
/// let a = Arbi::from_str_radix("123456789", 10).unwrap();
/// assert_eq!(a.size_base_ref(10), 9);
/// ```
Expand All @@ -176,7 +165,7 @@ impl Arbi {

pub(crate) fn size_radix_no_check(&mut self, base: u32) -> BitCount {
let mut count: BitCount = 0;
while self > 0 {
while self.size() != 0 {
Self::div_algo_digit_inplace(self, base as Digit);
count += 1;
}
Expand All @@ -192,7 +181,6 @@ impl Arbi {
}
if base.is_power_of_two() {
let bit_length = self.size_bits();
// let base_log2 = base.ilog2();
let base_log2 = u32::ilog2_(base);
return Some(BitCount::div_ceil_(
bit_length,
Expand Down
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