Continued fraction/Arithmetic/G(matrix ng, continued fraction n1, continued fraction n2): Difference between revisions
Continued fraction/Arithmetic/G(matrix ng, continued fraction n1, continued fraction n2) (view source)
Revision as of 16:43, 19 March 2023
, 1 year ago→Using multiple precision numbers
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The program closely follows the Standard ML code, so one can compare the two languages with each other. They have similar syntaxes, but are very different. Notice, for instance, that ATS has overloads, whereas SML does not. (SML has signatures with respective namespaces.) In ATS, a function is not a closure unless you explicitly make it one, whereas in SML no special notation is needed. And so on.
ATS is translated to C, and its functions (except closures) are essentially just C functions. One can write Arduino code and Linux kernel modules in ATS, because ATS is,
I have broken the program into three files, to demonstrate what an ATS program might look like, if it were broken into separately compiled parts.
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implement sqrt2 = silver_ratio - one
implement sqrt5 = (two * golden_ratio) - one
</syntaxhighlight>
The third file is the main program. It is called <code>continued-fraction-task.dats</code>:
<syntaxhighlight lang="ats">
(* Main program. *)
(*
Install ats2-xprelude, being sure to enable GMP support:
https://sourceforge.net/p/chemoelectric/ats2-xprelude
If you have it installed already, there might have been bugfixes
since. So try updating.
Then, to compile the program:
patscc -std=gnu2x -g -O2 -DATS_MEMALLOC_GCBDW \
$(pkg-config --cflags ats2-xprelude) \
$(pkg-config --variable=PATSCCFLAGS ats2-xprelude) \
continued-fraction-task.dats continued_fraction.{s,d}ats \
$(pkg-config --libs ats2-xprelude) -lgc -lm
*)
(* Load templates from the ATS2 prelude: *)
#include "share/atspre_staload.hats"
staload "continued_fraction.sats" (* Programmer access to exported stuff. *)
dynload "continued_fraction.dats" (* Initialize the "val". *)
(* Load declarations and templates from ats2-xprelude: *)
#include "xprelude/HATS/xprelude.hats"
staload "xprelude/SATS/exrat.sats"
staload _ = "xprelude/DATS/exrat.dats"
fn
make_pad (n : size_t) : string =
let
val n = g1ofg0 n
prval () = lemma_g1uint_param n
implement string_tabulate$fopr<> _ = ' '
in
strnptr2string (string_tabulate<> n)
end
fn
show_with_note (expression : string,
cf : continued_fraction,
note : string) : void =
let
val cf_str = cf2string cf
val expr_sz = strlen expression
and cf_sz = strlen cf_str
and note_sz = strlen note
val expr_pad_sz = max (i2sz 19 - expr_sz, i2sz 0)
and cf_pad_sz =
if iseqz note_sz then
i2sz 0
else
max (i2sz 48 - cf_sz, i2sz 0)
val expr_pad = make_pad expr_pad_sz
and cf_pad = make_pad cf_pad_sz
in
println! (expr_pad, expression, " => ",
cf_str, cf_pad, note)
end
fn
show_without_note (expression : string,
cf : continued_fraction) : void =
show_with_note (expression, cf, "")
overload show with show_with_note
overload show with show_without_note
implement
main0 () = (* A main that takes no arguments and returns 0. *)
begin
show ("golden ratio", golden_ratio, "(1 + sqrt(5))/2");
show ("silver ratio", silver_ratio, "(1 + sqrt(2))");
show ("sqrt2", sqrt2);
show ("sqrt5", sqrt5);
show ("1/4", one_fourth);
show ("1/3", one_third);
show ("1/2", one_half);
show ("2/3", two_thirds);
show ("3/4", three_fourths);
show ("13/11", r2cf (13, 11));
show ("22/7", r2cf (22, 7), "approximately pi");
show ("0", zero);
show ("1", one);
show ("2", two);
show ("3", three);
show ("4", four);
show ("4 + 3", four + three);
show ("4 - 3", four - three);
show ("4 * 3", four * three);
show ("4 / 3", four / three);
show ("4 ** 3", four ** 3);
show ("4 ** (-3)", four ** (~3));
show ("negative 4", ~four);
show ("(1 + 1/sqrt(2))/2",
(one + (one / sqrt2)) / two, "method 1");
show ("(1 + 1/sqrt(2))/2",
silver_ratio * (sqrt2 ** (~3)), "method 2");
show ("(1 + 1/sqrt(2))/2",
((silver_ratio ** 2) + one) / (four * two), "method 3");
show ("sqrt2 + sqrt2", sqrt2 + sqrt2);
show ("sqrt2 - sqrt2", sqrt2 - sqrt2);
show ("sqrt2 * sqrt2", sqrt2 * sqrt2);
show ("sqrt2 / sqrt2", sqrt2 / sqrt2);
end
</syntaxhighlight>
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