BigUint always use u64 as the internal machine unsigned integer
This change allow a speedup of ~1.5 on shootout-pidigits on a i32 system. `DoubleBigDigit` is used to abstract the internal unsigned integer used in computation to simplity future architecture specialization. `BigDigit::from_uint` and `BigDigit::to_uint` become `BigDigit::from_doublebigdigit` and `BigDigit::to_doublebigdigit`. [breaking-change]
This commit is contained in:
Guillaume Pinot
parent
239557de6d
commit
593f6a42d0
@ -31,50 +31,43 @@ use std::{i64, u64};
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/**
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A `BigDigit` is a `BigUint`'s composing element.
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A `BigDigit` is half the size of machine word size.
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*/
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#[cfg(target_word_size = "32")]
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pub type BigDigit = u16;
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pub type BigDigit = u32;
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/**
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A `BigDigit` is a `BigUint`'s composing element.
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A `BigDigit` is half the size of machine word size.
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A `DoubleBigDigit` is the internal type used to do the computations. Its
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size is the double of the size of `BigDigit`.
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*/
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#[cfg(target_word_size = "64")]
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pub type BigDigit = u32;
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pub type DoubleBigDigit = u64;
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pub static ZERO_BIG_DIGIT: BigDigit = 0;
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static ZERO_VEC: [BigDigit, ..1] = [ZERO_BIG_DIGIT];
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pub mod BigDigit {
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use super::BigDigit;
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use super::DoubleBigDigit;
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#[cfg(target_word_size = "32")]
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pub static bits: uint = 16;
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#[cfg(target_word_size = "64")]
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// `DoubleBigDigit` size dependent
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pub static bits: uint = 32;
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pub static base: uint = 1 << bits;
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static lo_mask: uint = (-1 as uint) >> bits;
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pub static base: DoubleBigDigit = 1 << bits;
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static lo_mask: DoubleBigDigit = (-1 as DoubleBigDigit) >> bits;
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#[inline]
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fn get_hi(n: uint) -> BigDigit { (n >> bits) as BigDigit }
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fn get_hi(n: DoubleBigDigit) -> BigDigit { (n >> bits) as BigDigit }
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#[inline]
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fn get_lo(n: uint) -> BigDigit { (n & lo_mask) as BigDigit }
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fn get_lo(n: DoubleBigDigit) -> BigDigit { (n & lo_mask) as BigDigit }
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/// Split one machine sized unsigned integer into two `BigDigit`s.
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/// Split one `DoubleBigDigit` into two `BigDigit`s.
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#[inline]
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pub fn from_uint(n: uint) -> (BigDigit, BigDigit) {
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pub fn from_doublebigdigit(n: DoubleBigDigit) -> (BigDigit, BigDigit) {
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(get_hi(n), get_lo(n))
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}
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/// Join two `BigDigit`s into one machine sized unsigned integer
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/// Join two `BigDigit`s into one `DoubleBigDigit`
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#[inline]
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pub fn to_uint(hi: BigDigit, lo: BigDigit) -> uint {
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(lo as uint) | ((hi as uint) << bits)
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pub fn to_doublebigdigit(hi: BigDigit, lo: BigDigit) -> DoubleBigDigit {
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(lo as DoubleBigDigit) | ((hi as DoubleBigDigit) << bits)
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}
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}
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@ -202,7 +195,8 @@ impl Add<BigUint, BigUint> for BigUint {
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let mut carry = 0;
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let mut sum: Vec<BigDigit> = a.data.iter().zip(b.data.iter().chain(zeros)).map(|(ai, bi)| {
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let (hi, lo) = BigDigit::from_uint((*ai as uint) + (*bi as uint) + (carry as uint));
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let (hi, lo) = BigDigit::from_doublebigdigit(
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(*ai as DoubleBigDigit) + (*bi as DoubleBigDigit) + (carry as DoubleBigDigit));
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carry = hi;
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lo
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}).collect();
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@ -219,8 +213,11 @@ impl Sub<BigUint, BigUint> for BigUint {
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let mut borrow = 0;
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let diff: Vec<BigDigit> = a.take(new_len).zip(b).map(|(ai, bi)| {
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let (hi, lo) = BigDigit::from_uint(
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BigDigit::base + (*ai as uint) - (*bi as uint) - (borrow as uint)
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let (hi, lo) = BigDigit::from_doublebigdigit(
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BigDigit::base
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+ (*ai as DoubleBigDigit)
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- (*bi as DoubleBigDigit)
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- (borrow as DoubleBigDigit)
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);
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/*
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hi * (base) + lo == 1*(base) + ai - bi - borrow
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@ -274,8 +271,8 @@ impl Mul<BigUint, BigUint> for BigUint {
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let mut carry = 0;
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let mut prod: Vec<BigDigit> = a.data.iter().map(|ai| {
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let (hi, lo) = BigDigit::from_uint(
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(*ai as uint) * (n as uint) + (carry as uint)
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let (hi, lo) = BigDigit::from_doublebigdigit(
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(*ai as DoubleBigDigit) * (n as DoubleBigDigit) + (carry as DoubleBigDigit)
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);
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carry = hi;
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lo
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@ -440,10 +437,10 @@ impl Integer for BigUint {
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let mut d = Vec::with_capacity(an.len());
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let mut carry = 0;
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for elt in an.iter().rev() {
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let ai = BigDigit::to_uint(carry, *elt);
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let di = ai / (bn as uint);
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let ai = BigDigit::to_doublebigdigit(carry, *elt);
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let di = ai / (bn as DoubleBigDigit);
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assert!(di < BigDigit::base);
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carry = (ai % (bn as uint)) as BigDigit;
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carry = (ai % (bn as DoubleBigDigit)) as BigDigit;
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d.push(di as BigDigit)
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}
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d.reverse();
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@ -515,39 +512,14 @@ impl ToPrimitive for BigUint {
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})
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}
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#[cfg(target_word_size = "32")]
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// `DoubleBigDigit` size dependent
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#[inline]
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fn to_u64(&self) -> Option<u64> {
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match self.data.len() {
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0 => Some(0),
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1 => Some(self.data.as_slice()[0] as u64),
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2 => {
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Some(BigDigit::to_uint(self.data.as_slice()[1], self.data.as_slice()[0]) as u64)
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}
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3 => {
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let n_lo = BigDigit::to_uint(self.data.as_slice()[1], self.data.as_slice()[0]) as
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u64;
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let n_hi = self.data.as_slice()[2] as u64;
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Some((n_hi << 32) + n_lo)
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}
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4 => {
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let n_lo = BigDigit::to_uint(self.data.as_slice()[1], self.data.as_slice()[0])
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as u64;
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let n_hi = BigDigit::to_uint(self.data.as_slice()[3], self.data.as_slice()[2])
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as u64;
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Some((n_hi << 32) + n_lo)
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}
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_ => None
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}
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}
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#[cfg(target_word_size = "64")]
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#[inline]
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fn to_u64(&self) -> Option<u64> {
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match self.data.len() {
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0 => Some(0),
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1 => Some(self.data.as_slice()[0] as u64),
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2 => Some(BigDigit::to_uint(self.data.as_slice()[1], self.data.as_slice()[0]) as u64),
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2 => Some(BigDigit::to_doublebigdigit(self.data.as_slice()[1], self.data.as_slice()[0])
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as u64),
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_ => None
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}
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}
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@ -565,26 +537,10 @@ impl FromPrimitive for BigUint {
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}
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}
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#[cfg(target_word_size = "32")]
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// `DoubleBigDigit` size dependent
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#[inline]
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fn from_u64(n: u64) -> Option<BigUint> {
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let n_lo = (n & 0x0000_0000_FFFF_FFFF) as uint;
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let n_hi = (n >> 32) as uint;
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let n = match (BigDigit::from_uint(n_hi), BigDigit::from_uint(n_lo)) {
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((0, 0), (0, 0)) => Zero::zero(),
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((0, 0), (0, n0)) => BigUint::new(vec!(n0)),
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((0, 0), (n1, n0)) => BigUint::new(vec!(n0, n1)),
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((0, n2), (n1, n0)) => BigUint::new(vec!(n0, n1, n2)),
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((n3, n2), (n1, n0)) => BigUint::new(vec!(n0, n1, n2, n3)),
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};
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Some(n)
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}
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#[cfg(target_word_size = "64")]
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#[inline]
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fn from_u64(n: u64) -> Option<BigUint> {
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let n = match BigDigit::from_uint(n as uint) {
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let n = match BigDigit::from_doublebigdigit(n) {
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(0, 0) => Zero::zero(),
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(0, n0) => BigUint::new(vec!(n0)),
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(n1, n0) => BigUint::new(vec!(n0, n1))
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@ -650,8 +606,8 @@ impl ToStrRadix for BigUint {
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}
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return fill_concat(convert_base(self, base).as_slice(), radix, max_len);
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fn convert_base(n: &BigUint, base: uint) -> Vec<BigDigit> {
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let divider = FromPrimitive::from_uint(base).unwrap();
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fn convert_base(n: &BigUint, base: DoubleBigDigit) -> Vec<BigDigit> {
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let divider = base.to_biguint().unwrap();
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let mut result = Vec::new();
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let mut m = n.clone();
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while m >= divider {
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@ -709,7 +665,7 @@ impl BigUint {
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/// Creates and initializes a `BigUint`.
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pub fn parse_bytes(buf: &[u8], radix: uint) -> Option<BigUint> {
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let (base, unit_len) = get_radix_base(radix);
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let base_num = match FromPrimitive::from_uint(base) {
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let base_num = match base.to_biguint() {
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Some(base_num) => base_num,
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None => { return None; }
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};
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@ -756,8 +712,8 @@ impl BigUint {
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let mut carry = 0;
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let mut shifted: Vec<BigDigit> = self.data.iter().map(|elem| {
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let (hi, lo) = BigDigit::from_uint(
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(*elem as uint) << n_bits | (carry as uint)
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let (hi, lo) = BigDigit::from_doublebigdigit(
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(*elem as DoubleBigDigit) << n_bits | (carry as DoubleBigDigit)
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);
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carry = hi;
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lo
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@ -797,33 +753,9 @@ impl BigUint {
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}
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}
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#[cfg(target_word_size = "32")]
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// `DoubleBigDigit` size dependent
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#[inline]
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fn get_radix_base(radix: uint) -> (uint, uint) {
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assert!(1 < radix && radix <= 16);
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match radix {
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2 => (65536, 16),
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3 => (59049, 10),
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4 => (65536, 8),
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5 => (15625, 6),
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6 => (46656, 6),
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7 => (16807, 5),
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8 => (32768, 5),
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9 => (59049, 5),
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10 => (10000, 4),
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11 => (14641, 4),
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12 => (20736, 4),
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13 => (28561, 4),
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14 => (38416, 4),
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15 => (50625, 4),
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16 => (65536, 4),
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_ => fail!()
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}
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}
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#[cfg(target_word_size = "64")]
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#[inline]
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fn get_radix_base(radix: uint) -> (uint, uint) {
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fn get_radix_base(radix: uint) -> (DoubleBigDigit, uint) {
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assert!(1 < radix && radix <= 16);
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match radix {
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2 => (4294967296, 32),
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@ -1599,36 +1531,7 @@ mod biguint_tests {
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"88887777666655554444333322221111");
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}
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#[cfg(target_word_size = "32")]
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#[test]
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fn test_convert_i64() {
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fn check(b1: BigUint, i: i64) {
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let b2: BigUint = FromPrimitive::from_i64(i).unwrap();
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assert!(b1 == b2);
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assert!(b1.to_i64().unwrap() == i);
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}
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check(Zero::zero(), 0);
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check(One::one(), 1);
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check(i64::MAX.to_biguint().unwrap(), i64::MAX);
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check(BigUint::new(vec!( )), 0);
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check(BigUint::new(vec!( 1 )), (1 << (0*BigDigit::bits)));
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check(BigUint::new(vec!(-1 )), (1 << (1*BigDigit::bits)) - 1);
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check(BigUint::new(vec!( 0, 1 )), (1 << (1*BigDigit::bits)));
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check(BigUint::new(vec!(-1, -1 )), (1 << (2*BigDigit::bits)) - 1);
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check(BigUint::new(vec!( 0, 0, 1 )), (1 << (2*BigDigit::bits)));
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check(BigUint::new(vec!(-1, -1, -1 )), (1 << (3*BigDigit::bits)) - 1);
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check(BigUint::new(vec!( 0, 0, 0, 1 )), (1 << (3*BigDigit::bits)));
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check(BigUint::new(vec!(-1, -1, -1, -1 >> 1)), i64::MAX);
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assert_eq!(i64::MIN.to_biguint(), None);
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assert_eq!(BigUint::new(vec!(-1, -1, -1, -1 )).to_i64(), None);
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assert_eq!(BigUint::new(vec!( 0, 0, 0, 0, 1)).to_i64(), None);
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assert_eq!(BigUint::new(vec!(-1, -1, -1, -1, -1)).to_i64(), None);
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}
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#[cfg(target_word_size = "64")]
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// `DoubleBigDigit` size dependent
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#[test]
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fn test_convert_i64() {
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fn check(b1: BigUint, i: i64) {
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@ -1653,35 +1556,7 @@ mod biguint_tests {
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assert_eq!(BigUint::new(vec!(-1, -1, -1)).to_i64(), None);
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}
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#[cfg(target_word_size = "32")]
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#[test]
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fn test_convert_u64() {
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fn check(b1: BigUint, u: u64) {
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let b2: BigUint = FromPrimitive::from_u64(u).unwrap();
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assert!(b1 == b2);
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assert!(b1.to_u64().unwrap() == u);
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}
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check(Zero::zero(), 0);
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check(One::one(), 1);
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check(u64::MIN.to_biguint().unwrap(), u64::MIN);
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check(u64::MAX.to_biguint().unwrap(), u64::MAX);
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check(BigUint::new(vec!( )), 0);
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check(BigUint::new(vec!( 1 )), (1 << (0*BigDigit::bits)));
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check(BigUint::new(vec!(-1 )), (1 << (1*BigDigit::bits)) - 1);
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check(BigUint::new(vec!( 0, 1 )), (1 << (1*BigDigit::bits)));
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check(BigUint::new(vec!(-1, -1 )), (1 << (2*BigDigit::bits)) - 1);
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check(BigUint::new(vec!( 0, 0, 1 )), (1 << (2*BigDigit::bits)));
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check(BigUint::new(vec!(-1, -1, -1 )), (1 << (3*BigDigit::bits)) - 1);
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check(BigUint::new(vec!( 0, 0, 0, 1)), (1 << (3*BigDigit::bits)));
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check(BigUint::new(vec!(-1, -1, -1, -1)), u64::MAX);
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assert_eq!(BigUint::new(vec!( 0, 0, 0, 0, 1)).to_u64(), None);
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assert_eq!(BigUint::new(vec!(-1, -1, -1, -1, -1)).to_u64(), None);
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}
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#[cfg(target_word_size = "64")]
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// `DoubleBigDigit` size dependent
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#[test]
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fn test_convert_u64() {
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fn check(b1: BigUint, u: u64) {
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