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Barry Schwartz
Barry Schwartz
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Extensions to, and bugfixes for, the ATS2 prelude.
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* Expanded support for integer types, and workarounds for
bugs. Changes include at least the following:
- I have added intmax and uintmax.
- I have worked around bugs in g1 versions of comparisons with
zero.
- I have tightened the postconditions of g1 versions of mod and
nmod.
- I have expanded the set of integer power routines, and implement
pre-compiled versions that are loop-free. (The behavior when
there is signed integer overflow may differ from that of the
prelude. I consider this unimportant, because signed integer
overflow is a bad thing.)
- I have added ‘true Euclidean division’ of signed integers,
where the remainder is always non-negative.
- I have added gcd.
- I have added ‘count trailing zeros’, ‘find first set’, ‘find
last set’, ‘population count’.
* Expanded support for floating point, and workarounds for bugs.
* Support for the following floating point types: float16, float32,
float64, float128, float16x float32x, float64x, float128x,
decimal32, decimal64, decimal128, decimal64x, decimal128x. Your C
compiler and libraries are likely to support some of these but not
others, in varying degrees. ¶ Footnote: On AMD64, the ldouble type
is stored on 128-bit boundaries, but it is NOT a 128-bit floating
point type. It is an 80-bit floating point type, which is stored on
32-bit boundaries on x86. If you want quad precision on AMD64, use
float128 (which requires libraries that come with GCC).
* 32+32-bit fixed point, treated as if it were floating point
(g0float).
* Optionally: exact rationals, via the GNU Multiple Precision
Arithmetic Library (GMP). These are a nonlinear type (for garbage
collection), and are treated as if they were floating point
(g0float). ¶ The exact rationals support ‘big integer’ operations on
their numerators, and thus you can represent a big integer as an
exrat with denominator one. ¶ If you enable exact rationals, you
also get ‘bisection iterators’. These can be useful when one
implements an algorithm that adaptively bisects intervals.
* Optionally: multiple precision floating point numbers, via the GNU
Multiple Precision Floating-Point Reliable Library (MPFR). As with
exact rationals, these are a nonlinear type (for garbage
collection), and are treated as if they were floating point
(g0float). ¶ Currently (and probably forever), if you enable
multiple precision floating point, you also must enable exact
rationals. However, this should be no problem, because MPFR itself
uses GMP: if you have the former, you most likely have the
latter. Furthermore, both are necessary to build GCC.
* Sorting, with algorithms selectable via -DATS flag.
---
References for some obscure integer algorithms, such as for counting
trailing zeros or ones, and calculating population count:
{{cite web
| title = Bit Twiddling Hacks
| url = https://graphics.stanford.edu/~seander/bithacks.html
| date = 2023-01-14
| archiveurl = http://archive.today/GNADt
| archivedate = 2023-01-14 }}
{{cite web
| title = BitScan - Chessprogramming wiki
| url = https://www.chessprogramming.org/index.php?title=BitScan&oldid=22495
| date = 2023-02-03
| archiveurl = http://archive.today/iPXfa
| archivedate = 2023-02-03 }}
The algorithms may appear in any of ATS, C, or m4 code.
---
Licensing:
This program is free software: you can redistribute it and/or
modify it under the terms of the GNU General Public License, as
published by the Free Software Foundation, either version 3 of the
License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
General Public License for more details.
You should have received copies of the GNU General Public License
along with this program. If not, see
<https://www.gnu.org/licenses/>.
---
