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Merge pull request #1571 from nbraud + rivy

perf/factor ~ deduplicate divisors
This commit is contained in:
Roy Ivy III 2020-10-26 15:28:46 -05:00
commit effb94b03e
7 changed files with 236 additions and 171 deletions

135
Cargo.lock generated
View file

@ -190,17 +190,27 @@ name = "const_fn"
version = "0.4.2"
source = "registry+https://github.com/rust-lang/crates.io-index"
[[package]]
name = "conv"
version = "0.3.3"
source = "registry+https://github.com/rust-lang/crates.io-index"
dependencies = [
"custom_derive 0.1.7 (registry+https://github.com/rust-lang/crates.io-index)",
]
[[package]]
name = "coreutils"
version = "0.0.1"
dependencies = [
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"filetime 0.2.12 (registry+https://github.com/rust-lang/crates.io-index)",
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"rand 0.7.3 (registry+https://github.com/rust-lang/crates.io-index)",
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"textwrap 0.11.0 (registry+https://github.com/rust-lang/crates.io-index)",
"time 0.1.42 (registry+https://github.com/rust-lang/crates.io-index)",
@ -476,6 +486,11 @@ dependencies = [
"memchr 2.3.3 (registry+https://github.com/rust-lang/crates.io-index)",
]
[[package]]
name = "custom_derive"
version = "0.1.7"
source = "registry+https://github.com/rust-lang/crates.io-index"
[[package]]
name = "data-encoding"
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@ -695,6 +710,11 @@ name = "match_cfg"
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source = "registry+https://github.com/rust-lang/crates.io-index"
[[package]]
name = "maybe-uninit"
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source = "registry+https://github.com/rust-lang/crates.io-index"
[[package]]
name = "md5"
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@ -914,24 +934,6 @@ dependencies = [
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[[package]]
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[[package]]
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@ -945,15 +947,6 @@ dependencies = [
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[[package]]
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[[package]]
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@ -984,14 +977,6 @@ dependencies = [
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[[package]]
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@ -1000,46 +985,6 @@ dependencies = [
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[[package]]
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[[package]]
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[[package]]
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@ -1048,14 +993,6 @@ dependencies = [
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[[package]]
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[[package]]
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@ -1079,14 +1016,6 @@ dependencies = [
"num_cpus 1.13.0 (registry+https://github.com/rust-lang/crates.io-index)",
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[[package]]
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"rand_core 0.3.1 (registry+https://github.com/rust-lang/crates.io-index)",
]
[[package]]
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@ -1243,6 +1172,14 @@ dependencies = [
"generic-array 0.8.3 (registry+https://github.com/rust-lang/crates.io-index)",
]
[[package]]
name = "smallvec"
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dependencies = [
"maybe-uninit 2.0.0 (registry+https://github.com/rust-lang/crates.io-index)",
]
[[package]]
name = "strsim"
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@ -1639,6 +1576,7 @@ dependencies = [
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"uucore_procs 0.0.4 (git+https://github.com/uutils/uucore.git?branch=canary)",
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@ -2569,6 +2507,7 @@ dependencies = [
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@ -2584,6 +2523,7 @@ dependencies = [
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@ -2615,6 +2555,7 @@ dependencies = [
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@ -2643,24 +2584,15 @@ dependencies = [
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View file

@ -329,10 +329,12 @@ pin_same-file = { version="1.0.4, < 1.0.6", package="same-file" } ## same-file v
pin_winapi-util = { version="0.1.2, < 0.1.3", package="winapi-util" } ## winapi-util v0.1.3 has compiler errors for MinRustV v1.32.0, expects 1.34
[dev-dependencies]
conv = "0.3"
filetime = "0.2"
libc = "0.2"
rand = "0.6"
rand = "0.7"
regex = "1.0"
sha1 = { version="0.6", features=["std"] }
tempfile = "3.1"
time = "0.1"
unindent = "0.1"

View file

@ -18,6 +18,7 @@ num-traits = "0.2" # used in src/numerics.rs, which is included by build.rs
[dependencies]
num-traits = "0.2"
rand = { version="0.7", features=["small_rng"] }
smallvec = { version="0.6.13, < 1.0" }
uucore = { version="0.0.4", package="uucore", git="https://github.com/uutils/uucore.git", branch="canary" }
uucore_procs = { version="0.0.4", package="uucore_procs", git="https://github.com/uutils/uucore.git", branch="canary" }

View file

@ -7,33 +7,44 @@
extern crate rand;
use smallvec::SmallVec;
use std::cell::RefCell;
use std::fmt;
use crate::numeric::{Arithmetic, Montgomery};
use crate::numeric::{gcd, Arithmetic, Montgomery};
use crate::{miller_rabin, rho, table};
type Exponent = u8;
#[derive(Clone, Debug)]
struct Decomposition(Vec<(u64, Exponent)>);
struct Decomposition(SmallVec<[(u64, Exponent); NUM_FACTORS_INLINE]>);
// The number of factors to inline directly into a `Decomposition` object.
// As a consequence of the ErdősKac theorem, the average number of prime factors
// of integers < 10²⁵ ≃ 2⁸³ is 4, so we can use a slightly higher value.
const NUM_FACTORS_INLINE: usize = 5;
impl Decomposition {
fn one() -> Decomposition {
Decomposition(Vec::new())
Decomposition(SmallVec::new())
}
fn add(&mut self, factor: u64, exp: Exponent) {
debug_assert!(exp > 0);
// Assert the factor doesn't already exist in the Decomposition object
debug_assert_eq!(self.0.iter_mut().find(|(f, _)| *f == factor), None);
if let Some((_, e)) = self.0.iter_mut().find(|(f, _)| *f == factor) {
*e += exp;
} else {
self.0.push((factor, exp))
}
self.0.push((factor, exp))
}
fn is_one(&self) -> bool {
self.0.is_empty()
}
fn pop(&mut self) -> Option<(u64, Exponent)> {
self.0.pop()
}
#[cfg(test)]
fn product(&self) -> u64 {
self.0
.iter()
@ -77,11 +88,11 @@ impl Factors {
self.0.borrow_mut().add(prime, exp)
}
#[cfg(test)]
pub fn push(&mut self, prime: u64) {
self.add(prime, 1)
}
#[cfg(test)]
fn product(&self) -> u64 {
self.0.borrow().product()
}
@ -102,62 +113,116 @@ impl fmt::Display for Factors {
}
}
fn _factor<A: Arithmetic + miller_rabin::Basis>(num: u64, f: Factors) -> Factors {
fn _find_factor<A: Arithmetic + miller_rabin::Basis>(num: u64) -> Option<u64> {
use miller_rabin::Result::*;
// Shadow the name, so the recursion automatically goes from “Big” arithmetic to small.
let _factor = |n, f| {
if n < (1 << 32) {
_factor::<Montgomery<u32>>(n, f)
} else {
_factor::<A>(n, f)
}
};
if num == 1 {
return f;
}
let n = A::new(num);
let divisor = match miller_rabin::test::<A>(n) {
Prime => {
let mut r = f;
r.push(num);
return r;
}
Composite(d) => d,
Pseudoprime => rho::find_divisor::<A>(n),
};
let f = _factor(divisor, f);
_factor(num / divisor, f)
match miller_rabin::test::<A>(n) {
Prime => None,
Composite(d) => Some(d),
Pseudoprime => Some(rho::find_divisor::<A>(n)),
}
}
pub fn factor(mut n: u64) -> Factors {
fn find_factor(num: u64) -> Option<u64> {
if num < (1 << 32) {
_find_factor::<Montgomery<u32>>(num)
} else {
_find_factor::<Montgomery<u64>>(num)
}
}
pub fn factor(num: u64) -> Factors {
let mut factors = Factors::one();
if n < 2 {
if num < 2 {
return factors;
}
let z = n.trailing_zeros();
if z > 0 {
factors.add(2, z as Exponent);
n >>= z;
let mut n = num;
let n_zeros = num.trailing_zeros();
if n_zeros > 0 {
factors.add(2, n_zeros as Exponent);
n >>= n_zeros;
}
debug_assert_eq!(num, n * factors.product());
if n == 1 {
return factors;
}
let (factors, n) = table::factor(n, factors);
table::factor(&mut n, &mut factors);
debug_assert_eq!(num, n * factors.product());
if n < (1 << 32) {
_factor::<Montgomery<u32>>(n, factors)
} else {
_factor::<Montgomery<u64>>(n, factors)
if n == 1 {
return factors;
}
let mut dec = Decomposition::one();
dec.add(n, 1);
while !dec.is_one() {
// Check correctness invariant
debug_assert_eq!(num, factors.product() * dec.product());
let (factor, exp) = dec.pop().unwrap();
if let Some(divisor) = find_factor(factor) {
let mut gcd_queue = Decomposition::one();
let quotient = factor / divisor;
let mut trivial_gcd = quotient == divisor;
if trivial_gcd {
gcd_queue.add(divisor, exp + 1);
} else {
gcd_queue.add(divisor, exp);
gcd_queue.add(quotient, exp);
}
while !trivial_gcd {
debug_assert_eq!(factor, gcd_queue.product());
let mut tmp = Decomposition::one();
trivial_gcd = true;
for i in 0..gcd_queue.0.len() - 1 {
let (mut a, exp_a) = gcd_queue.0[i];
let (mut b, exp_b) = gcd_queue.0[i + 1];
if a == 1 {
continue;
}
let g = gcd(a, b);
if g != 1 {
trivial_gcd = false;
a /= g;
b /= g;
}
if a != 1 {
tmp.add(a, exp_a);
}
if g != 1 {
tmp.add(g, exp_a + exp_b);
}
if i + 1 != gcd_queue.0.len() - 1 {
gcd_queue.0[i + 1].0 = b;
} else if b != 1 {
tmp.add(b, exp_b);
}
}
gcd_queue = tmp;
}
debug_assert_eq!(factor, gcd_queue.product());
dec.0.extend(gcd_queue.0);
} else {
// factor is prime
factors.add(factor, exp);
}
}
factors
}
#[cfg(test)]
@ -165,6 +230,19 @@ mod tests {
use super::{factor, Factors};
use quickcheck::quickcheck;
#[test]
fn factor_correctly_recombines_prior_test_failures() {
let prior_failures = [
// * integers with duplicate factors (ie, N.pow(M))
4566769_u64, // == 2137.pow(2)
2044854919485649_u64,
18446739546814299361_u64,
18446738440860217487_u64,
18446736729316206481_u64,
];
assert!(prior_failures.iter().all(|i| factor(*i).product() == *i));
}
#[test]
fn factor_recombines_small() {
assert!((1..10_000)
@ -172,6 +250,15 @@ mod tests {
.all(|i| factor(i).product() == i));
}
#[test]
fn factor_recombines_small_squares() {
// factor(18446736729316206481) == 4294966441 ** 2 ; causes debug_assert fault for repeated decomposition factor in add()
// ToDO: explain/combine with factor_18446736729316206481 and factor_18446739546814299361 tests
assert!((1..10_000)
.map(|i| (2 * i + 1) * (2 * i + 1))
.all(|i| factor(i).product() == i));
}
#[test]
fn factor_recombines_overflowing() {
assert!((0..250)
@ -182,7 +269,7 @@ mod tests {
#[test]
fn factor_recombines_strong_pseudoprime() {
// This is a strong pseudoprime (wrt. miller_rabin::BASIS)
// and triggered a bug in rho::factor's codepath handling
// and triggered a bug in rho::factor's code path handling
// miller_rabbin::Result::Composite
let pseudoprime = 17179869183;
for _ in 0..20 {
@ -213,7 +300,7 @@ impl quickcheck::Arbitrary for Factors {
let mut n = u64::MAX;
// Adam Kalai's algorithm for generating uniformly-distributed
// integers and their factorisation.
// integers and their factorization.
//
// See Generating Random Factored Numbers, Easily, J. Cryptology (2003)
'attempt: loop {

View file

@ -79,7 +79,11 @@ mod tests {
fn divisor(a: u64, b: u64) -> bool {
// Test that gcd(a, b) divides a and b
let g = gcd(a, b);
(g != 0 && a % g == 0 && b % g == 0) || (g == 0 && a == 0 && b == 0)
if g != 0 {
a % g == 0 && b % g == 0
} else {
a == 0 && b == 0 // for g == 0
}
}
fn commutative(a: u64, b: u64) -> bool {

View file

@ -14,7 +14,8 @@ use crate::Factors;
include!(concat!(env!("OUT_DIR"), "/prime_table.rs"));
pub(crate) fn factor(mut num: u64, mut factors: Factors) -> (Factors, u64) {
pub(crate) fn factor(n: &mut u64, factors: &mut Factors) {
let mut num = *n;
for &(prime, inv, ceil) in P_INVS_U64 {
if num == 1 {
break;
@ -42,5 +43,5 @@ pub(crate) fn factor(mut num: u64, mut factors: Factors) -> (Factors, u64) {
}
}
(factors, num)
*n = num;
}

View file

@ -6,34 +6,64 @@
// that was distributed with this source code.
use crate::common::util::*;
use std::time::SystemTime;
#[path = "../../src/uu/factor/sieve.rs"]
mod sieve;
extern crate conv;
extern crate rand;
use self::rand::distributions::{Distribution, Uniform};
use self::rand::{rngs::SmallRng, Rng, SeedableRng};
use self::sieve::Sieve;
extern crate rand;
use self::rand::distributions::{Distribution, Uniform};
use self::rand::{rngs::SmallRng, FromEntropy, Rng};
const NUM_PRIMES: usize = 10000;
const LOG_PRIMES: f64 = 14.0; // ceil(log2(NUM_PRIMES))
const NUM_TESTS: usize = 100;
#[test]
fn test_first_100000_integers() {
extern crate sha1;
let n_integers = 100_000;
let mut instring = String::new();
for i in 0..=n_integers {
instring.push_str(&(format!("{} ", i))[..]);
}
println!("STDIN='{}'", instring);
let result = new_ucmd!().pipe_in(instring.as_bytes()).run();
let stdout = result.stdout;
assert!(result.success);
// `seq 0 100000 | factor | sha1sum` => "4ed2d8403934fa1c76fe4b84c5d4b8850299c359"
let hash_check = sha1::Sha1::from(stdout.as_bytes()).hexdigest();
assert_eq!(hash_check, "4ed2d8403934fa1c76fe4b84c5d4b8850299c359");
}
#[test]
fn test_random() {
use conv::prelude::*;
let log_num_primes = f64::value_from(NUM_PRIMES).unwrap().log2().ceil();
let primes = Sieve::primes().take(NUM_PRIMES).collect::<Vec<u64>>();
let mut rng = SmallRng::from_entropy();
println!("(seed) rng={:?}", rng);
let rng_seed = SystemTime::now()
.duration_since(SystemTime::UNIX_EPOCH)
.unwrap()
.as_secs();
println!("rng_seed={:?}", rng_seed);
let mut rng = SmallRng::seed_from_u64(rng_seed);
let mut rand_gt = move |min: u64| {
let mut product = 1u64;
let mut product = 1_u64;
let mut factors = Vec::new();
while product < min {
// log distribution---higher probability for lower numbers
let factor;
loop {
let next = rng.gen_range(0f64, LOG_PRIMES).exp2().floor() as usize;
let next = rng.gen_range(0_f64, log_num_primes).exp2().floor() as usize;
if next < NUM_PRIMES {
factor = primes[next];
break;
@ -73,9 +103,14 @@ fn test_random() {
#[test]
fn test_random_big() {
let mut rng = SmallRng::from_entropy();
println!("(seed) rng={:?}", rng);
let bitrange_1 = Uniform::new(14usize, 51);
let rng_seed = SystemTime::now()
.duration_since(SystemTime::UNIX_EPOCH)
.unwrap()
.as_secs();
println!("rng_seed={:?}", rng_seed);
let mut rng = SmallRng::seed_from_u64(rng_seed);
let bitrange_1 = Uniform::new(14_usize, 51);
let mut rand_64 = move || {
// first, choose a random number of bits for the first factor
let f_bit_1 = bitrange_1.sample(&mut rng);
@ -85,11 +120,11 @@ fn test_random_big() {
// we will have a number of additional factors equal to nfacts + 1
// where nfacts is in [0, floor(rem/14) ) NOTE half-open interval
// Each prime factor is at least 14 bits, hence floor(rem/14)
let nfacts = Uniform::new(0usize, rem / 14).sample(&mut rng);
let nfacts = Uniform::new(0_usize, rem / 14).sample(&mut rng);
// we have to distribute extrabits among the (nfacts + 1) values
let extrabits = rem - (nfacts + 1) * 14;
// (remember, a Range is a half-open interval)
let extrarange = Uniform::new(0usize, extrabits + 1);
let extrarange = Uniform::new(0_usize, extrabits + 1);
// to generate an even split of this range, generate n-1 random elements
// in the range, add the desired total value to the end, sort this list,
@ -116,7 +151,7 @@ fn test_random_big() {
let f_bits = f_bits;
let mut nbits = 0;
let mut product = 1u64;
let mut product = 1_u64;
let mut factors = Vec::new();
for bit in f_bits {
assert!(bit < 37);
@ -161,6 +196,8 @@ fn test_big_primes() {
}
fn run(instring: &[u8], outstring: &[u8]) {
println!("STDIN='{}'", String::from_utf8_lossy(instring));
println!("STDOUT(expected)='{}'", String::from_utf8_lossy(outstring));
// now run factor
new_ucmd!()
.pipe_in(instring)