From dad1df6c1ab8fa06e9c5a28a6849e61fcdaa5008 Mon Sep 17 00:00:00 2001 From: Robin Kruppe Date: Wed, 30 Dec 2015 14:01:42 +0100 Subject: [PATCH] Speed up dec2flt fast path with additional tables. Add tables of small powers of ten used in the fast path. The tables are redundant: We could also use the big, more accurate table and round the value to the correct type (in fact we did just that before this commit). However, the rounding is extra work and slows down the fast path. Because only very small exponents enter the fast path, the table and thus the space overhead is negligible. Speed-wise, this is a clear win on a [benchmark] comparing the fast path to a naive, hand-optimized, inaccurate algorithm. Specifically, this change narrows the gap from a roughly 5x difference to a roughly 3.4x difference. [benchmark]: https://gist.github.com/Veedrac/dbb0c07994bc7882098e --- src/etc/dec2flt_table.py | 35 +++++++++++++++++---- src/libcore/num/dec2flt/algorithm.rs | 10 ++---- src/libcore/num/dec2flt/rawfp.rs | 12 ++++++++ src/libcore/num/dec2flt/table.rs | 46 ++++++++++++++++++++++++++-- 4 files changed, 88 insertions(+), 15 deletions(-) diff --git a/src/etc/dec2flt_table.py b/src/etc/dec2flt_table.py index b0140fb2455..9fdab1fcfca 100644 --- a/src/etc/dec2flt_table.py +++ b/src/etc/dec2flt_table.py @@ -25,6 +25,7 @@ even larger, and it's already uncomfortably large (6 KiB). """ from __future__ import print_function import sys +from math import ceil, log from fractions import Fraction from collections import namedtuple @@ -33,7 +34,6 @@ N = 64 # Size of the significand field in bits MIN_SIG = 2 ** (N - 1) MAX_SIG = (2 ** N) - 1 - # Hand-rolled fp representation without arithmetic or any other operations. # The significand is normalized and always N bit, but the exponent is # unrestricted in range. @@ -92,7 +92,7 @@ def error(f, e, z): ulp_err = abs_err / Fraction(2) ** z.exp return float(ulp_err) -LICENSE = """ +HEADER = """ // Copyright 2015 The Rust Project Developers. See the COPYRIGHT // file at the top-level directory of this distribution and at // http://rust-lang.org/COPYRIGHT. @@ -102,9 +102,23 @@ LICENSE = """ // , at your // option. This file may not be copied, modified, or distributed // except according to those terms. + +//! Tables of approximations of powers of ten. +//! DO NOT MODIFY: Generated by `src/etc/dec2flt_table.py` """ + def main(): + print(HEADER.strip()) + print() + print_proper_powers() + print() + print_short_powers(32, 24) + print() + print_short_powers(64, 53) + + +def print_proper_powers(): MIN_E = -305 MAX_E = 305 e_range = range(MIN_E, MAX_E+1) @@ -114,13 +128,10 @@ def main(): err = error(1, e, z) assert err < 0.5 powers.append(z) - typ = "([u64; {0}], [i16; {0}])".format(len(e_range)) - print(LICENSE.strip()) - print("// Table of approximations of powers of ten.") - print("// DO NOT MODIFY: Generated by a src/etc/dec2flt_table.py") print("pub const MIN_E: i16 = {};".format(MIN_E)) print("pub const MAX_E: i16 = {};".format(MAX_E)) print() + typ = "([u64; {0}], [i16; {0}])".format(len(powers)) print("pub const POWERS: ", typ, " = ([", sep='') for z in powers: print(" 0x{:x},".format(z.sig)) @@ -130,5 +141,17 @@ def main(): print("]);") +def print_short_powers(num_bits, significand_size): + max_sig = 2**significand_size - 1 + # The fast path bails out for exponents >= ceil(log5(max_sig)) + max_e = int(ceil(log(max_sig, 5))) + e_range = range(max_e) + typ = "[f{}; {}]".format(num_bits, len(e_range)) + print("pub const F", num_bits, "_SHORT_POWERS: ", typ, " = [", sep='') + for e in e_range: + print(" 1e{},".format(e)) + print("];") + + if __name__ == '__main__': main() diff --git a/src/libcore/num/dec2flt/algorithm.rs b/src/libcore/num/dec2flt/algorithm.rs index 1f0f06d7461..82d3389edc4 100644 --- a/src/libcore/num/dec2flt/algorithm.rs +++ b/src/libcore/num/dec2flt/algorithm.rs @@ -60,17 +60,13 @@ pub fn fast_path(integral: &[u8], fractional: &[u8], e: i64) -> Opt if f > T::max_sig() { return None; } - let e = e as i16; // Can't overflow because e.abs() <= LOG5_OF_EXP_N // The case e < 0 cannot be folded into the other branch. Negative powers result in // a repeating fractional part in binary, which are rounded, which causes real // (and occasioally quite significant!) errors in the final result. - // The case `e == 0`, however, is unnecessary for correctness. It's just measurably faster. - if e == 0 { - Some(T::from_int(f)) - } else if e > 0 { - Some(T::from_int(f) * fp_to_float(power_of_ten(e))) + if e >= 0 { + Some(T::from_int(f) * T::short_fast_pow10(e as usize)) } else { - Some(T::from_int(f) / fp_to_float(power_of_ten(-e))) + Some(T::from_int(f) / T::short_fast_pow10(e.abs() as usize)) } } diff --git a/src/libcore/num/dec2flt/rawfp.rs b/src/libcore/num/dec2flt/rawfp.rs index 19758974003..2099c6a7baa 100644 --- a/src/libcore/num/dec2flt/rawfp.rs +++ b/src/libcore/num/dec2flt/rawfp.rs @@ -37,6 +37,7 @@ use num::diy_float::Fp; use num::FpCategory::{Infinite, Zero, Subnormal, Normal, Nan}; use num::Float; use num::dec2flt::num::{self, Big}; +use num::dec2flt::table; #[derive(Copy, Clone, Debug)] pub struct Unpacked { @@ -73,6 +74,9 @@ pub trait RawFloat : Float + Copy + Debug + LowerExp /// represented, the other code in this module makes sure to never let that happen. fn from_int(x: u64) -> Self; + /// Get the value 10^e from a pre-computed table. Panics for e >= ceil_log5_of_max_sig(). + fn short_fast_pow10(e: usize) -> Self; + // FIXME Everything that follows should be associated constants, but taking the value of an // associated constant from a type parameter does not work (yet?) // A possible workaround is having a `FloatInfo` struct for all the constants, but so far @@ -175,6 +179,10 @@ impl RawFloat for f32 { x as f32 } + fn short_fast_pow10(e: usize) -> Self { + table::F32_SHORT_POWERS[e] + } + fn max_normal_digits() -> usize { 35 } @@ -222,6 +230,10 @@ impl RawFloat for f64 { x as f64 } + fn short_fast_pow10(e: usize) -> Self { + table::F64_SHORT_POWERS[e] + } + fn max_normal_digits() -> usize { 305 } diff --git a/src/libcore/num/dec2flt/table.rs b/src/libcore/num/dec2flt/table.rs index dd985fd155b..cb8c94313d0 100644 --- a/src/libcore/num/dec2flt/table.rs +++ b/src/libcore/num/dec2flt/table.rs @@ -7,8 +7,10 @@ // , at your // option. This file may not be copied, modified, or distributed // except according to those terms. -// Table of approximations of powers of ten. -// DO NOT MODIFY: Generated by a src/etc/dec2flt_table.py + +//! Tables of approximations of powers of ten. +//! DO NOT MODIFY: Generated by `src/etc/dec2flt_table.py` + pub const MIN_E: i16 = -305; pub const MAX_E: i16 = 305; @@ -1237,3 +1239,43 @@ pub const POWERS: ([u64; 611], [i16; 611]) = ([ 946, 950, ]); + +pub const F32_SHORT_POWERS: [f32; 11] = [ + 1e0, + 1e1, + 1e2, + 1e3, + 1e4, + 1e5, + 1e6, + 1e7, + 1e8, + 1e9, + 1e10, +]; + +pub const F64_SHORT_POWERS: [f64; 23] = [ + 1e0, + 1e1, + 1e2, + 1e3, + 1e4, + 1e5, + 1e6, + 1e7, + 1e8, + 1e9, + 1e10, + 1e11, + 1e12, + 1e13, + 1e14, + 1e15, + 1e16, + 1e17, + 1e18, + 1e19, + 1e20, + 1e21, + 1e22, +];