When autoloading a Maxima script, avoid clobbering global state.

[maxima.git] / tests / rtest_translator.mac

/* A nice test of the translator would be to translate the entire test suite ...
 * In the meantime here are some tests to verify some specific bugs are fixed.
 */

(kill (all), 0);
0;

/* There are various cases where (by design) translate and compile don't
 * signal an error when a function fails to translate.  So here we define
 * translate_or_lose and compile_or_lose so we don't have to explicitly
 * check the return values of translate and compile in every test.
 *
 * Passing `all' or `functions' is not supported.  I'm not sure how much
 * sense those make here for tests, but something could be added later if
 * a test really wants them for some reason.
 */
block ([translate : false],
  local (make_tester),
  make_tester (trfun) ::=
    buildq ([trfun, name : concat (trfun, '_or_lose)],
      (name (['fns]) :=
         block ([ret : apply ('trfun, fns), losers : []],
           if ret # fns then
             /* Report failures in the same order as the given args */
             (for f in fns do if not (member (f, ret)) then push (f, losers),
              error ('trfun, "failed unexpectedly for", reverse (losers))),
           fns),
       /* Prevent this from being killed during kill(all), etc.
        * We can remove this later if we're more precise about
        * what we're killing throughout this file.
        */
       ?mfunction\-delete ('name, functions))),
  make_tester (translate),
  make_tester (compile),
  0);
0;

/* SF [ 1728888 ] translator bugs: no mnot mprogn */

(foo (e,v) := block([vi], for vi in v while not(emptyp(e)) do (print(vi), e : rest(e)), e),
 foo ([1, 2, 3], [a, b]));
[3];

(translate_or_lose (foo), foo ([1, 2, 3], [a, b]));
[3];

/* simpler function featuring mprogn and mnot */

(bar (x) := (x : 2*x, x : 3*x, not (x < 100)), bar (3));
false;

(translate_or_lose (bar), bar (3));
false;

/* SF [ 1646525 ] no function mdoin */

(try_me(x) := block([acc : 0], for i in x while i > 5 do acc : acc + i, acc),
 try_me ([10, 9, 8, 7, 6, 5, 4, 5, 6, 7, 8, 9, 10]));
40;

(translate_or_lose (try_me), try_me ([10, 9, 8, 7, 6, 5, 4, 5, 6, 7, 8, 9, 10]));
40;

/* SF [ 1818645 ] Compiled maxima code containing $ARRAY gets a Lisp error. */

(test_array_comp (x) :=
  block ([abc, i],
    array (abc, 3),
    for i thru 3 do (abc[i]: i*i),
    abc[3] : x, 
    [abc, abc[3], abc[2]]),
  test_array_comp (100));
[abc, 100, 4];

(translate_or_lose (test_array_comp), test_array_comp (100));
[abc, 100, 4];

/* SF [ 545794 ] Local Array does not compile properly */

(trial (a) :=
  block ([myvar, i],
    local(myvar),
    array (myvar, 7),
    for i : 0 thru 7 do myvar [i] : a^i,
    [member (myvar, arrays), listarray (myvar)]),
 trial (2));
[true, [1, 2, 4, 8, 16, 32, 64, 128]];

(translate_or_lose (trial), trial (2));
[true, [1, 2, 4, 8, 16, 32, 64, 128]];

/* This next test used to fail because local properties would leak out
 * in the translated case.  This test is expected to pass now.  There
 * are more local tests below for bug #2976.
 */

[member (myvar, arrays), errcatch (listarray (myvar))];
[false, []];

/* for loop variable not special
 * reported to mailing list 2009-08-13 "Why won't this compile?"
 */

(kill (foo1, bar1),
 foo1 () := bar1 + 1,
 baz1 (n) := block ([S : 0], for bar1:0 thru n - 1 do S : S + foo1 (), S),
 translate_or_lose (baz1),
 baz1 (10));
55;

/* original example */

(fun(A,b,s,VF,x,h):= block
 ([Y],
   Y[1]:  x,
   for i:2 thru s do
    Y[i]:  x + h*(sum(A[i,j]*VF(Y[j]),j,1,i-1)),
   x: expand(x + h*sum(b[i]*VF(Y[i]),i,1,s))),
  A: matrix([1,1],[1,1]),
  b: [1,1],
 0);
0;

fun(A,b,2,f,[1,1],.01);
0.01*f(0.01*f([1,1])+[1,1])+0.01*f([1,1])+[1,1]$

(translate_or_lose (fun), fun(A,b,2,f,[1,1],.01));
0.01*f(0.01*f([1,1])+[1,1])+0.01*f([1,1])+[1,1]$

/* incorrect code emitted for call from translated function to untranslated
 * SF bug # 2934064 "problem loading ezunits"
 */

(f0001 (x) := [f0002 (x), f0003 (x)],
 f0002 (x) := x,
 f0003 (x) := x,
 translate_or_lose (f0002, f0001),
 f0001 (1));
[1, 1];

(translate_or_lose (f0003), f0001 (1));
[1, 1];

(compile_or_lose (f0003), f0001 (1));
[1, 1];

(compile_or_lose (f0003, f0002, f0001), f0001 (1));
[1, 1];

/* SF bug # 2938716 "too much evaluation in translated code"
 */

(g0001 (x) := [g0002 (x), g0003 (x)],
 g0002 (x) := x,
 g0003 (x) := x,
 translate_or_lose (g0002, g0001),
 kill (aa, bb, cc),
 aa : 'bb,
 bb : 'cc,
 g0001 (aa));
[bb, bb];

(translate_or_lose (g0003), g0001 (aa));
[bb, bb];

(compile_or_lose (g0003), g0001 (aa));
[bb, bb];

(compile_or_lose (g0003, g0002, g0001), g0001 (aa));
[bb, bb];

/* SF bug # 3035313 "some array references translated incorrectly"
 */

(kill (aa1, aa3, bb1, bb3, cc1, cc3),
 array (aa1, 15),
 array (aa3, 12, 4, 6),
 array (bb1, flonum, 15),
 array (bb3, flonum, 5, 6, 7),
 array (cc1, fixnum, 8),
 array (cc3, fixnum, 6, 10, 4),
 0);
0;

(kill (faa, gaa, fbb, gbb, fcc, gcc),
 faa (n) := aa1[n] + aa3[n, n - 1, n - 2],
 gaa (n) := (aa1[n] : 123, aa3[n, n - 1, n - 2] : 321),
 fbb (n) := bb1[n] + bb3[n, n - 1, n - 2],
 gbb (n) := (bb1[n] : 123, bb3[n, n - 1, n - 2] : 321),
 fcc (n) := cc1[n] + cc3[n, n - 1, n - 2],
 gcc (n) := (cc1[n] : 123, cc3[n, n - 1, n - 2] : 321),
 0);
0;

[gaa (4), gbb (4), gcc (4)];
[321, 321, 321];

[faa (4), fbb (4), fcc (4)];
[444, 444, 444];

translate_or_lose (faa, gaa, fbb, gbb, fcc, gcc);
[faa, gaa, fbb, gbb, fcc, gcc];

[gaa (4), gbb (4), gcc (4)];
[321, 321, 321];

[faa (4), fbb (4), fcc (4)];
[444, 444, 444];

compile_or_lose (faa, gaa, fbb, gbb, fcc, gcc);
[faa, gaa, fbb, gbb, fcc, gcc];

[gaa (4), gbb (4), gcc (4)];
[321, 321, 321];

[faa (4), fbb (4), fcc (4)];
[444, 444, 444];

/* try same stuff again w/ undeclared arrays ...
 * no type spec => only one kind of array
 */

(kill (aa1, aa3, bb1, bb3, cc1, cc3),
 ?fmakunbound (faa),
 ?fmakunbound (fbb),
 [gaa (4), faa (4)]);
[321, 444];

(translate_or_lose (faa, gaa), [gaa (4), faa (4)]);
[321, 444];

(compile_or_lose (faa, gaa), [gaa (4), faa (4)]);
[321, 444];

/* try same stuff again w/ Lisp arrays */

(kill (aa1, aa3, bb1, bb3, cc1, cc3),
 map (?fmakunbound, [faa, fbb, fcc, gaa, gbb, gcc]),
 aa1 : make_array (any, 15),
 aa3 : make_array (any, 12, 4, 6),
 bb1 : make_array (flonum, 15),
 bb3 : make_array (flonum, 5, 6, 7),
 cc1 : make_array (fixnum, 8),
 cc3 : make_array (fixnum, 6, 10, 4),
 0);
0;

[gaa (4), gbb (4), gcc (4)];
[321, 321, 321];

[faa (4), fbb (4), fcc (4)];
[444, 444, 444];

translate_or_lose (faa, gaa, fbb, gbb, fcc, gcc);
[faa, gaa, fbb, gbb, fcc, gcc];

[gaa (4), gbb (4), gcc (4)];
[321, 321, 321];

[faa (4), fbb (4), fcc (4)];
[444, 444, 444];

compile_or_lose (faa, gaa, fbb, gbb, fcc, gcc);
[faa, gaa, fbb, gbb, fcc, gcc];

[gaa (4), gbb (4), gcc (4)];
[321, 321, 321];

[faa (4), fbb (4), fcc (4)];
[444, 444, 444];

/* SF bug # 2569: "translate rat(1,x) and rat([1]) incorrect" */

(kill (f), f () := rat (x, x), translate_or_lose (f), f ());
''(rat (x, x));

(kill (f), f () := rat ([1]), translate_or_lose (f), f ());
''(rat ([1]));

(kill (foo, y1a, y1b, y2a, y2b), 
  foo(x) := block (mode_declare (x, float),
     [tanh (x), tan (x), sech (x), sec (x), acos (x), acot (x), sin (x),
      acsc (x), asinh (x), acsch (x), cosh (x), coth (x), realpart (x),
      asec (x), asin (x), erf (x), log (x), cos (x), cot (x), csc (x),
      sinh (x), csch (x), sqrt (x), exp (x)]),
  0);
0;

y1a : foo (0.5);
[.4621171572600097,.5463024898437905,0.886818883970074,1.139493927324549,
 1.047197551196597,1.107148717794091,0.479425538604203,
 1.570796326794897-1.316957896924817*%i,.4812118250596035,1.44363547517881,
 1.127625965206381,2.163953413738653,0.5,1.316957896924817*%i,
 0.523598775598299,.5204998778130465,-.6931471805599453,.8775825618903728,
 1.830487721712452,2.085829642933488,.5210953054937474,1.919034751334944,
 .7071067811865476,1.648721270700128]$

y1b : foo (1.5);
[.9051482536448664,14.10141994717172,.4250960349422805,14.1368329029699,
 .9624236501192069*%i,.5880026035475675,.9974949866040544,.7297276562269662,
 1.194763217287109,.6251451172504168,2.352409615243247,1.104791392982512,1.5,
 .8410686705679303,1.570796326794897-.9624236501192069*%i,.9661051464753108,
 .4054651081081644,0.0707372016677029,.07091484430265245,1.002511304246725,
 2.129279455094817,.4696424405952246,1.224744871391589,4.481689070338065]$

y1c : foo (1.0);
[0.7615941559557649,1.557407724654902,0.6480542736638855,
 1.850815717680925,0.0,0.7853981633974483,0.8414709848078965,
 1.570796326794897,0.881373587019543,0.881373587019543,
 1.543080634815244,1.313035285499331,1.0,0.0,1.570796326794897,
 0.8427007929497148,0.0,0.5403023058681398,0.6420926159343306,
 1.188395105778121,1.175201193643801,0.8509181282393216,1.0,
 2.718281828459045]$

(translate_or_lose (foo), y2a : foo (0.5), y2b : foo (1.5), 0);
0;

is (y1a = y2a);
true;

is (y1b = y2b);
true;

block ([tr_float_can_branch_complex : false],
  translate_or_lose (foo),
  y2c : foo (1.0),
  0);
0;

is (y1c = y2c);
true;

/* verify that save/compfile/compile_file/translate_file preserves upper/lower case in symbol names */

/* save */

(kill (all),
 foo (x) := my_foo * x,
 Foo (x) := my_Foo * x,
 FOO (x) := my_FOO * x,
 [my_foo, my_Foo, my_FOO] : [123, 456, 789],
 results : [foo (2), Foo (3), FOO (4)],
 my_test () := is (results = [2*123, 3*456, 4*789]),
 lisp_name : ssubst ("_", " ", build_info()@lisp_name),
 lisp_filename : sconcat (maxima_tempdir, "/tmp-rtest_translator-save-", lisp_name, ".lisp"),
 save (lisp_filename, values, functions),
 kill (allbut (lisp_filename)),
 load (lisp_filename),
 my_test ());
true;

/* compfile */

(kill (all),
 foo (x) := my_foo * x,
 Foo (x) := my_Foo * x,
 FOO (x) := my_FOO * x,
 lisp_name : ssubst ("_", " ", build_info()@lisp_name),
 lisp_filename : sconcat (maxima_tempdir, "/tmp-rtest_translator-compfile-", lisp_name, ".lisp"),
 compfile (lisp_filename, functions),
 kill (functions), 
 load (lisp_filename),
 [my_foo, my_Foo, my_FOO] : [123, 456, 789],
 results : [foo (2), Foo (3), FOO (4)],
 my_test () := is (results = [2*123, 3*456, 4*789]),
 my_test ());
true;
 
/* compile_file */

/* skip this test (and fail) if Lisp = ECL because stream i/o causes "stack smashing" error
 * see: https://sourceforge.net/p/maxima/bugs/3291/
 */
if build_info()@lisp_name # "ECL" then
(kill (all),
 lisp_name : ssubst ("_", " ", build_info()@lisp_name),
 maxima_filename : sconcat (maxima_tempdir, "/tmp-rtest_translator-compile_file-", lisp_name, ".mac"),
 fasl_filename : sconcat (maxima_tempdir, "/tmp-rtest_translator-compile_file-", lisp_name, ".fasl"),
 lisp_filename : sconcat (maxima_tempdir, "/tmp-rtest_translator-compile_file-", lisp_name, ".LISP"),
 maxima_output : openw (maxima_filename),
 maxima_content :
"foo (x) := my_foo * x;
Foo (x) := my_Foo * x;
FOO (x) := my_FOO * x;
[my_foo, my_Foo, my_FOO] : [123, 456, 789];
results : [foo (2), Foo (3), FOO (4)];
my_test () := is (results = [2*123, 3*456, 4*789]);",
 printf (maxima_output, maxima_content),
 close (maxima_output),
 compile_file (maxima_filename, fasl_filename, lisp_filename),
 kill (allbut (lisp_filename)),
 load (lisp_filename),
 my_test ());
true;

/* translate_file */

/* skip this test (and fail) if Lisp = ECL because stream i/o causes "stack smashing" error
 * see: https://sourceforge.net/p/maxima/bugs/3291/
 */
if build_info()@lisp_name # "ECL" then
(kill (all),
 lisp_name : ssubst ("_", " ", build_info()@lisp_name),
 maxima_filename : sconcat (maxima_tempdir, "/tmp-rtest_translator-translate_file-", lisp_name, ".mac"),
 lisp_filename : sconcat (maxima_tempdir, "/tmp-rtest_translator-translate_file-", lisp_name, ".LISP"),
 maxima_output : openw (maxima_filename),
 maxima_content :
"foo (x) := my_foo * x;
Foo (x) := my_Foo * x;
FOO (x) := my_FOO * x;
[my_foo, my_Foo, my_FOO] : [123, 456, 789];
results : [foo (2), Foo (3), FOO (4)];
my_test () := is (results = [2*123, 3*456, 4*789]);",
 printf (maxima_output, maxima_content),
 close (maxima_output),
 translate_file (maxima_filename, lisp_filename),
 kill (allbut (lisp_filename)),
 load (lisp_filename),
 my_test ());
true;

/* Bug 2934:

   Translating a literal exponent that comes out as a float shouldn't
   produce assigned type any. This test runs the translation for a
   trivial function that triggered the bug then looks in the unlisp
   file (which contains messages from the translator) and checks that
   there aren't any warnings.
*/
/* skip this test (and fail) if Lisp = ECL because stream i/o causes "stack smashing" error
 * see: https://sourceforge.net/p/maxima/bugs/3291/
 */
if build_info()@lisp_name # "ECL" then
(kill (all),
 lisp_name : ssubst ("_", " ", build_info()@lisp_name),
 basename: sconcat (maxima_tempdir, "/tmp-rtest_translator-2934-", lisp_name),
 maxima_filename : sconcat (basename, ".mac"),
 lisp_filename : sconcat (basename, ".LISP"),
 maxima_output : openw (maxima_filename),
 maxima_content : "f () := block([y], mode_declare(y,float), y: 3^0.33, y)$",
 printf (maxima_output, maxima_content),
 close (maxima_output),
 translate_file (maxima_filename, lisp_filename),
 kill (allbut(basename)),
 /* Any warning messages end up at .UNLISP */
 block ([unlisp: openr (sconcat (basename, ".UNLISP")),
         line, acc: []],
   while stringp (line: readline(unlisp)) do
     if is ("warning" = split(line, ":")[1]) then push(line, acc),
   acc));
[]$

/* makelist translated incorrectly
 * SF bug #3083: "Error on compiling a working maxima function"
 */

(kill(all),
 f1(n) := makelist (1, n),
 f2(n) := makelist (i^2, i, n),
 f3(l) := makelist (i^3, i, l),
 f4(n) := makelist (i^4, i, 1, n),
 f5(m, n) := makelist (i^5, i, 1, n, m),
 translate_or_lose(f1, f2, f3, f4, f5),
 0);
0;

f1(5);
[1,1,1,1,1];

f2(5);
[1, 4, 9, 16, 25];

f3([1,2,3]);
[1, 8, 27];

f4(4);
[1, 16, 81, 256];

f5(2, 10);
[1, 243, 3125, 16807, 59049];

/* original function from bug report */

(ordersort(lis,vars,oper):=block([negsumdispflag:false,liss:lis,varlist:vars,temp], /*Does lexicographical sort */
 for i:1 thru length(varlist) do (
     for j:1 thru i do (
         liss:sort(liss,lambda([x,y],apply("and",map(oper,makelist(part(x,2)[k],k,1,i)
                             ,makelist(part(y,2)[k],k,1,i)))))
     )),liss),
 translate_or_lose (ordersort),
 [member ('transfun, properties (ordersort)),
  ordersort([[-7,[0,2,1]],[3,[1,2,1]],[1,[0,4,1]],[6,[4,3,3]],[6,[4,4,3]],
             [-7,[3,5,4]],[2,[0,0,5]],[-10,[2,2,5]],[-10,[3,4,7]],[7,[3,8,9]]],
             [x,y,z],
             ">=")]);
[true,
 [[6,[4,4,3]],[6,[4,3,3]],[7,[3,8,9]],[-7,[3,5,4]],[-10,[3,4,7]],
  [-10,[2,2,5]],[3,[1,2,1]],[1,[0,4,1]],[-7,[0,2,1]],[2,[0,0,5]]]];

/* 'define' translated incorrectly, reported to mailing list circa 2017-01-24 */

(kill(foo, bar, baz, quux, mumble, blurf, umm, f, x, y),
 foo(y) := define(bar(x), x + y),
 baz(f, y) := define(funmake(f, [x]), x + y),
 quux() := (mumble(x) := 1 + x),
 [foo(10), baz(blurf, 20), quux()]);
/* note that results match because rhs of ":=" isn't simplified */
[bar(x) := 10 + x, blurf(x) := 20 + x, mumble(x) := 1 + x];

[bar(5), blurf(5), mumble(5)];
[15, 25, 6];

(kill(bar, blurf, mumble),
 translate_or_lose(foo, baz, quux),
 [foo(11), baz(umm, 21), quux()]);
/* note that results match because rhs of ":=" isn't simplified */
[bar(x) := 11 + x, umm(x) := 21 + x, mumble(x) := 1 + x];

makelist (is (x # false), x, map (?fboundp, [foo, baz, quux])); /* test for generalized Boolean value */
[true, true, true];

[bar(5), umm(5), mumble(5)];
[16, 26, 6];

/* mailing list 2017-03-04: "An example that is broken by compile()"
 * translated code tickles a bug elsewhere (bug not in translator)
 */

(kill(fun, trigfunc, t1),
 fun():=block([trigfunc],
        trigfunc:lambda([cur],cur>t1),
        apply('trigfunc,[1])),
 0);
0;

/* I (Robert Dodier) believe this result should be trigfunc(1),
 * but, in any event, interpreted and compiled code should agree.
 * But if MAPPLY1 is ever changed, we can adjust these results.
 */
fun();
1 > t1;

(compile_or_lose(fun), fun());
1 > t1;

(kill(fun, trigfunc, t1),
 fun():=block([trigfunc],
        trigfunc:lambda([cur],cur>t1),
        apply(trigfunc,[1])),
 0);
0;

fun();
1 > t1;

(compile_or_lose(fun), fun());
1 > t1;

/* Verify that we catch malformed lambda expressions during translation.
 * More checks need to be added to the translator and more tests need to
 * be added here.
 */

/* no parameter list */
(kill (f),
 f () := lambda (),
 translate (f))$
[];

/* empty body */
(kill (f),
 f () := lambda ([x]),
 translate (f))$
[];

/* non-symbol in parameter list */
(kill (f),
 f () := lambda ([42], 'foo),
 translate (f))$
[];

/* misplaced "rest" parameter */
(kill (f),
 f () := lambda ([[l], x], 'foo),
 translate (f))$
[];

/* invalid "rest" parameter */
(kill (f),
 f () := lambda ([[l1, l2]], 'foo),
 translate (f))$
[];

/* attempting to bind a constant;
 * now OK, after commit 0517895
 */
block ([c, f],
  local (c, f),
  declare (c, constant),
  f () := lambda ([c], c),
  translate_or_lose (f))$
[f];

/* Verify that parameter/variable lists cannot contain duplicate variables.
 *
 * We only test a couple of cases here.  Many more tests for non-translated
 * code are in rtest2.  Do we want to test them all here as well?
 */

(kill(f),
 f () := lambda ([x, [x]], x),
 translate (f))$
[];

(kill(f),
 f () := block ([x, x:'foo], x),
 translate (f))$
[];

/* ensure that a null OPERATORS property doesn't interfere with
 * translation of local variable used as a function name.
 * This is the bug that caused failures in rtest_fractals when executed after run_testsuite.
 */

(kill(aa, foobarbaz, mumbleblurf, hhh),
 matchdeclare (aa, all),
 tellsimp (mumbleblurf(aa), 1 - aa),
 kill (mumbleblurf), /* as of 2018-01-28, this leaves (OPERATORS NIL) in property list */
 hhh(mumbleblurf, u) := mumbleblurf(u),
 foobarbaz(x) := 100 + x,
 translate_or_lose (hhh),
 hhh (foobarbaz, 11));
111;

/* SF bug report #3402: "Unbinding defined variable generates error in compiled functions" */

define_variable (zorble, 0, fixnum);
0;

(kill(f), f() := block ([zorble], 42), f());
42;

(translate_or_lose(f), f());
42;

/* bug reported to mailing list 2018-12-03: "error in compiling function with global variable" */

(test_f():= block( [a,b,c,d], niceindicespref:[a,b,c,d], disp("ciao"), return() ),
 0);
0;

(test_f (), niceindicespref);
[a,b,c,d];

(reset (niceindicespref),
 niceindicespref);
[i,j,k,l,m,n];

(translate_or_lose (test_f),
 test_f (),
 niceindicespref);
[a,b,c,d];

(reset (niceindicespref), 0);
0;

/* additional tests with variables which have ASSIGN property */

(set_error_stuff_permanently () :=
  block (error_syms : '[myerr1, myerr2, myerr3], error_size : 40),
 set_error_stuff_temporarily() :=
   block([error_syms : '[myerror1, myerror2, myerror3], error_size : 55],
         [error_syms, error_size]),
 0);
0;

(reset (error_syms, error_size),
 set_error_stuff_permanently (),
 [error_syms, error_size]);
[[myerr1, myerr2, myerr3], 40];

(reset (error_syms, error_size),
 translate_or_lose (set_error_stuff_permanently),
 set_error_stuff_permanently (),
 [error_syms, error_size]);
[[myerr1, myerr2, myerr3], 40];

(reset (error_syms, error_size),
 set_error_stuff_temporarily());
[[myerror1, myerror2, myerror3], 55];

[error_syms, error_size];
[[errexp1, errexp2, errexp3], 60];

(translate_or_lose (set_error_stuff_temporarily),
 set_error_stuff_temporarily());
[[myerror1, myerror2, myerror3], 55];

[error_syms, error_size];
[[errexp1, errexp2, errexp3], 60];

(kill(all), reset(), 0);
0;

/* SF bug #3412: "Bug when translating functions that contain an \"if\" (in my case an implicit if)" */

(f(x):=if cabs(1/(x+1)) < 1 then 1/(x+1) else 1,
 f(x + %i*y));
if 1/sqrt(y^2+(x+1)^2) < 1 then 1/(%i*y+x+1) else 1;

makelist (f(xy[1] + %i*xy[2]), xy, [[0, 0], [0, 1], [1, 1], [1, 0], [0, 2], [2, 2], [2, 0]]);
[1, 1/(%i+1), 1/(%i+2), 1/2, 1/(2*%i+1), 1/(2*%i+3), 1/3]$

(compile_or_lose (f),
 errcatch (f(x + %i*y)));
[];

'(f(x + %i*y));
f(x + %i*y);

makelist (f(xy[1] + %i*xy[2]), xy, [[0, 0], [0, 1], [1, 1], [1, 0], [0, 2], [2, 2], [2, 0]]);
[1, 1/(%i+1), 1/(%i+2), 1/2, 1/(2*%i+1), 1/(2*%i+3), 1/3]$

(if draw_version = 'draw_version then load (draw),
 draw3d(contour='map,
        proportional_axes=xy,
        nticks=100,
        contour_levels=20,
        explicit('(f(x+%i*y)),x,-2,2,y,-2,2)),
 0);
0;

/* nested if example -- note top-level "if" doesn't have an "else" clause, so the result is sometimes 'false' */

(g(a, b, c) := if a + b > c
                 then (if a > c
                         then (if b > c
                                 then (a + b + c)
                                 elseif b > c/2
                                   then (a - b - c)
                                   else (b - a - c))
                         else (a/2)),
 0);
0;

(aa: [3,9/4,5/4,11/4,1,0,9/4,1/4,5/2,9/4,3,5/2],
 bb: [3/2,3,1/4,3/4,5/2,7/4,5/2,3/4,1/2,3,13/4,7/2],
 cc: [7/2,15/4,5/2,5/4,15/4,1,1/4,7/4,2,11/4,1/4,7/4],
 map (g, aa, bb, cc));
[3/2,9/8,false,3/4,false,0,5,false,-4,9/8,13/2,31/4]$

(translate_or_lose (g),
 map (g, aa, bb, cc));
[3/2,9/8,false,3/4,false,0,5,false,-4,9/8,13/2,31/4]$

errcatch (g(1, 1, z));
[];

/* SF bug #3556: "5.43.0 translate / compile error"
 * Ensure that "if" within lambda is translated correctly.
 * The fix for #3412 tickled this bug.
 */

(kill (f),
 f(x, m) := map (lambda ([u], if m > 0 then u^m), [x, 2*x, 3*x]),
 0);
0;

is (?fboundp (f) # false);
false;

(kill (y),
 [f(y, 2), f(y, -2)]);
[[y^2, 4*y^2, 9*y^2], [false, false, false]];

(kill (n),
 errcatch (f(10, n)));
/* ensure that conditional expressions get simplified to expunge $FALSE ... sigh. */
''([[if n > 0 then 10^n, if n > 0 then 20^n, if n > 0 then 30^n]]);

(translate_or_lose (f),
 is (?fboundp (f) # false)); /* test for generalized Boolean value */
true;

[f(y, 2), f(y, -2)];
[[y^2, 4*y^2, 9*y^2], [false, false, false]];

errcatch (f(10, n));
[];

/* apply2 was translated incorrectly for several years.  applyb2
 * was translated incorrectly for decades.
 */

(defrule (foorule, foo (), 1),
 f () := apply2 ('(foo ()), foorule),
 translate_or_lose (f),
 f ());
1;

(defrule (barrule, bar (), 2),
 g () := applyb2 ('(bar ()), barrule),
 translate_or_lose (g),
 g ());
2;

(kill (foorule, f, barrule, g), 0);
0;

/* atan and atan2 calls with float arguments were translated
 * incorrectly for over a decade.  atan always caused a lisp error
 * and atan2 had a range between 0 and 2*%pi that was inconsistent
 * with the interpreted and non-float cases (where the range is
 * between -%pi and %pi).
 */

(foo () := [atan2 (-1.0, -1.0), atan2 (-1.0, 1.0)],
 translate_or_lose (foo),
 foo ());
[-2.356194490192345, -0.7853981633974483];

(bar () := atan (-1.0),
 translate_or_lose (bar),
 bar ());
-0.7853981633974483;

(kill (foo, bar), 0);
0;

/* The translation of a signum call with a float argument was
 * inconsistent when compared to the interpreted case and other
 * translated cases.  signum should return an integer or a float
 * when given an integer or a float argument, respectively.
 */

(foo () := [signum (0),  signum (0.0),
            signum (2),  signum (2.0),
            signum (-3), signum (-3.0)],
 translate_or_lose (foo),
 foo ());
[0, 0.0, 1, 1.0, -1, -1.0];

(kill (foo), 0);
0;

/* The translation of declare was broken for decades.  It worked
 * under Maclisp, but it had never worked under Common Lisp.
 */

(foo () := declare (n, integer, [x, y], noninteger),
 translate_or_lose (foo),
 foo (),
 [?kindp (n, integer),
  ?kindp (n, noninteger),
  ?kindp (x, integer),
  ?kindp (x, noninteger),
  ?kindp (y, integer),
  ?kindp (y, noninteger)]);
[true, false, false, true, false, true];

(kill (foo, n, x, y), 0);
0;

/* If a variable was declared to be of mode rational, then a lisp
 * error could occur during translation when attempting to convert
 * it to a float.
 */

(foo (x) := (mode_declare (x, rational), float (x)),
 bar (y) := (mode_declare (y, rational), 1.0 + y),
 translate_or_lose (foo, bar),
 [foo (1/4), bar (1/2)]);
[0.25, 1.5];

(kill (foo, bar, x, y), 0);
0;

/* The translation of an atan2 call with one float and one rational
 * argument was broken because the rational was not converted to a
 * float before calling ATAN.
 */

(foo () :=
   [atan2 (0.0, -1/2),
    atan2 (-1/2, 0.0),
    atan2 (0.0, -1),
    atan2 (1, 0.0)],
 bar (y, x) := (mode_declare (x, float, y, rational), atan2 (y, x)),
 l1 : [foo (), bar (1/3, 0.0)],
 translate_or_lose (foo, bar),
 l2 : [foo (), bar (1/3, 0.0)],
 is (l1 = l2));
true;

(kill (foo, bar, x, y, l1, l2), 0);
0;

/* When attempting to apply float contagion to the arguments, some
 * translations of max and min with mixed float and rational arguments
 * were broken because the rationals were not converted to floats before
 * calling MAX or MIN (like atan2 above).  Also, due to implementation-
 * dependent behavior in the underlying lisp regarding what to return
 * from MAX and MIN, the wrong mode could be used during translation and
 * some of the translations were possibly inconsistent with interpreted
 * cases.
 */

(foo (x) :=
   (mode_declare (x, rational),
    [max (),         min (),
     max (1),        min (1),
     max (1.0),      min (1.0),
     max (9/10),     min (9/10),
     max (x)   ,     min (x),
     max (0.0, 1),   min (0.0, 1),
     max (0, 1),     min (0, 1),
     max (1.0, 1),   min (1.0, 1),
     max (1, 1.0),   min (1, 1.0),
     max (2.0, 3.0), min (2.0, 3.0),
     max (-1, 1/2),  min (-1, 1/2),
     max (3/4, 1/2), min (3/4, 1/2),
     max (0.0, 1/2), min (0.0, 1/2),
     max (0, x),     min (0, x),
     max (-1.0, x),  min (-1.0, x),
     max (5/6, x),   min (5/6, x),
     max (x, 1),     min (x, 1)]),
 l1 : foo (2/3),
 translate_or_lose (foo),
 l2 : foo (2/3),
 is (l1 = l2));
true;

(kill (foo, x, l1, l2), 0);
0;

/* log and sqrt did not honor tr_float_can_branch_complex */

(foo (x) :=
   (mode_declare (x, float),
    [log  (-1.0), log  (x),
     sqrt (-1.0), sqrt (x)]),
 /* l1 is a list of Maxima complex numbers */
 l1 : foo (-2.0),
 some (lambda ([x], freeof (%i, x)), l1));
false;

block ([tr_float_can_branch_complex : false],
  translate_or_lose (foo),
  /* l2 is a list of lisp complex numbers because we told the
   * translator to assume the return values of log and sqrt
   * would not be complex, and it correctly returned the complex
   * numbers returned by LOG and SQRT directly.
   */
  l2 : foo (-2.0),
  [every (?complexp, l2),
   every ("#", l1, l2)]);
[true,
 true];

block ([tr_float_can_branch_complex : true],
  translate_or_lose (foo),
  /* l3 is a list of Maxima complex numbers because we told the
   * translator to assume the return values of log and sqrt
   * could be complex, and it converted the lisp complex numbers
   * returned by LOG and SQRT to Maxima complex numbers.
   */
  l3 : foo (-2.0),
  every (lambda ([x, y], cabs (x - y) < 1e-15), l1, l3));
true;

(kill (foo, x, l1, l2, l3), 0);
0;

/* The translations for evaluating = and # expressions to boolean
 * values with one float argument and a different numerical argument
 * (e.g. a fixnum) gave bogus results because the translator was
 * incorrectly applying float contagion to the arguments.
 */

(foo (s, w, x, y, z) :=
  (mode_declare (w, number, x, fixnum, y, flonum),
   [/* These translate to EQL comparisons */
    is (1 = 1),                 is (1 # 1),
    is (1 = 1.0),               is (1 # 1.0),
    is (1 = float (1)),         is (1 # float (1)),
    is (1.0 = float (1)),       is (1.0 # float (1)),
    is (w = 2),                 is (w # 2),
    is (w = 2.0),               is (w # 2.0),
    is (x = 3),                 is (x # 3),
    is (x = 3.0),               is (x # 3.0),
    is (x = float (3)),         is (x # float (3)),
    is (x = float (x)),         is (x # float (x)),
    is (y = 4),                 is (y # 4),
    is (y = 4.0),               is (y # 4.0),
    is (y = float (4)),         is (y # float (4)),
    is (y = float (y)),         is (y # float (y)),
    /* These translate to LIKE comparisons */
    is (z = 5),                 is (z # 5),
    is (z = 5.0),               is (z # 5.0),
    is (z = float (5)),         is (z # float (5)),
    is (z = float (z)),         is (z # float (z)),
    is (1/2 = 1/2),             is (1/2 # 1/2),
    is (1/2 = rat (1/2)),       is (1/2 # rat (1/2)),
    is (rat (1/2) = rat (1/2)), is (rat (1/2) # rat (1/2)),
    is (1/2 = 0.5),             is (1/2 # 0.5),
    is (1/2 = float (1/2)),     is (1/2 # float (1/2)),
    is (%i = %i),               is (%i # %i),
    is (1 + %i = 1 + %i),       is (1 + %i # 1 + %i),
    is (s = s),                 is (s # s),
    is (s = 'bar),              is (s # 'bar),
    is (s = 1),                 is (s # 1),
    is (s = 1.0),               is (s # 1.0),
    is (s = 1/2),               is (s # 1/2),
    is ('f (0) = 'f (0)),       is ('f (0) # 'f (0)),
    is ('g (s) = 'g (s)),       is ('g (s) # 'g (s)),
    is ('h (w) = 'h (w)),       is ('h (w) # 'h (w)),
    is ('i (x) = 'i (x)),       is ('i (x) # 'i (x)),
    is ('j (y) = 'j (y)),       is ('j (y) # 'j (y)),
    is ('k (z) = 'k (z)),       is ('k (z) # 'k (z))]),
 l1 : foo ('bar, 2, 3, 4.0, 5),
 translate_or_lose (foo),
 l2 : foo ('bar, 2, 3, 4.0, 5),
 [every (lambda ([x], ?typep (x, ?boolean)), l2),
  is (l1 = l2)]);
[true,
 true];

(kill (foo, w, x, y, l1, l2), 0);
0;

/* Bug #3048: notequal is not translated properly
 *
 * notequal expressions were only generically translated like user
 * function calls and the use of notequal in translated code caused
 * a runtime warning about it being totally undefined.  Also the
 * evaluation of notequal expressions to boolean values (via is, if,
 * etc.) were translated like the evaluation of an unknown predicate.
 */

(assume (equal (a, b), notequal (c, d)),
 foo () :=
  [is (equal (1, 1)),
   is (notequal (1, 1)),
   is (equal (1, 1.0)),
   is (notequal (1, 1.0)),
   is (equal (1, 1.0b0)),
   is (notequal (1, 1.0b0)),
   is (equal (1/2, 0.5)),
   is (notequal (1/2, 0.5)),
   is (equal (1/2, 0.5b0)),
   is (notequal (1/2, 0.5b0)),
   is (equal (1, 2)),
   is (notequal (1, 2)),
   is (equal ('ind, 'ind)),
   is (notequal ('ind, 'ind)),
   is (equal ('und, 'und)),
   is (notequal ('und, 'und)),
   is (equal ('a, 'b)),
   is (notequal ('a, 'b)),
   is (equal ('c, 'd)),
   is (notequal ('c, 'd)),
   is (equal (x^2 - 1, (x + 1) * (x - 1))),
   is (notequal (x^2 - 1, (x + 1) * (x - 1)))],
 l1 : foo (),
 translate_or_lose (foo),
 l2 : foo (),
 [every (lambda ([x], ?typep (x, ?boolean)), l2),
  is (l1 = l2)]);
[true,
 true];

(kill (foo, l1, l2),
 forget (equal (a, b), notequal (c, d)),
 0);
0;

/* The translation of a call to random with a float argument could
 * cause the generation of bogus code because this always had the
 * mode of fixnum.
 */

(foo (w, x, y, z) :=
  (mode_declare (w, fixnum, x, float),
   [[random (10),
     random (w),
     random (y)],
    [random (1.0),
     random (x),
     random (z),
     random (x) / 2,
     random (z) / 2,
     1 / (1 + random (x))],
    [random (10) / 2,
     random (w) / 3,
     random (y) / 4,
     1 / (1 + random (w)),
     1 / (1 + random (y))]]),
 translate_or_lose (foo),
 l : foo (50, 5.0, 100, 10.0),
 [every (integerp, first (l)),
  every (floatnump, second (l)),
  every (ratnump, third (l))]);
[true,
 true,
 true];

(kill (foo, w, x, l), 0);
0;

/* acosh, asech, atanh and acoth now have special translations for
 * float arguments.  These all honor tr_float_can_branch_complex.
 */

(foo (x) :=
   (mode_declare (x, float),
    [acosh (x), asech (x), atanh (x)]),
 bar (x) :=
   (mode_declare (x, float),
    [acoth (x)]),
 /* l1 is a list of Maxima complex numbers */
 l1 : append (foo (-3.0), foo (-2.0), bar (-0.5), bar (0.5)),
 some (lambda ([x], freeof (%i, x)), l1));
false;

block ([tr_float_can_branch_complex : false],
  translate_or_lose (foo, bar),
  /* l2 is a list of lisp complex numbers because we told the
   * translator to assume the return values would not be complex,
   * and it correctly returned the lisp complex numbers directly.
   */
  l2 : append (foo (-3.0), foo (-2.0), bar (-0.5), bar (0.5)),
  [every (?complexp, l2),
   every ("#", l1, l2),
   every ("=", l1, map (?complexify, l2))]);
[true,
 true,
 true];

block ([tr_float_can_branch_complex : true],
  translate_or_lose (foo, bar),
  /* l3 is a list of Maxima complex numbers because we told the
   * translator to assume the return values could be complex, and
   * it converted the lisp complex numbers to Maxima complex numbers.
   */
  l3 : append (foo (-3.0), foo (-2.0), bar (-0.5), bar (0.5)),
  every ("=", l1, l3));
true;

(kill (foo, bar, x, l1, l2, l3), 0);
0;

/* Bug #3642: Lisp error when translating assume
 *
 * Translating an assume call with an atomic argument would cause a
 * lisp error during translation.
 */

(foo () :=
   block ([ctx : supcontext (),
           x : a > 0,
           y : b > 0,
           r],
     assume (x, y, equal (c, 0)),
     r : [is (a > 0), is (b < 0), is (equal (c, 0))],
     killcontext (ctx),
     r),
 translate_or_lose (foo),
 foo ());
[true, false, true];

(kill (foo), 0);
0;

/* The translation of errcatch was broken because the mode of the
 * whole form was always assumed to be the same as the mode of the
 * last subform.  Since errcatch always yields a list, lisp errors
 * could easily occur.
 */

(foo () :=
   block ([listarith : true],
     [errcatch (1),
      1 + errcatch (2),
      1.0 * errcatch (2.0),
      errcatch (error ("oops")),
      errcatch (?error ("oops")),
      errcatch (1 / 0)]),
 translate_or_lose (foo),
 foo ());
[[1],
 [3],
 [2.0],
 [],
 [],
 []];

(kill (foo), 0);
0;

/* Attempting to translate multiple functions containing local would
 * cause an error.  Similarly, translating the same function multiple
 * times would cause an error if that function contained local.
 */

(foo () := local (), /* just something with local (not within a block) */
 bar () := local (), /* something else with local (not within a block) */
 translate_or_lose (foo),
 translate_or_lose (bar),
 translate_or_lose (foo, bar));
[foo, bar];

(kill (foo, bar), 0);
0;

/* Bug #2976: "local" doesn't work in translated code
 *
 * For decades no attempt was being made to clean up any local
 * properties.
 */

/* The internal LOCLIST used by local should be empty right now */
?null (?loclist);
true;

(f0 () := "one",
 foo1 () :=
   (local (f0),
    f0 () := "two",
    f0 ()),
 translate_or_lose (foo1),
 block ([v : foo1 ()],
   [f0 (), v]));
["one", "two"];

(kill (f0, foo1), 0);
0;

(arr1 [0] : "three",
 foo2 () :=
   block ([g : lambda ([],
                 local (arr1, arr2),
                 arr1 [0] : "four",
                 arr2 [5] : "five",
                 [arr1 [0],
                  arr2 [5],
                  arrayinfo (arr2)])],
     apply (g, [])),
 translate_or_lose (foo2),
 block ([v : foo2 ()],
   [arr1 [0],
    v,
    errcatch (arrayinfo (arr2))]));
["three",
 ["four",
  "five",
  [hashed, 1, [5]]],
 []];

(kill (arr1, foo2), 0);
0;

(foo3 (n) :=
   (local (h),
    h () := n + 1,
    if n = 10 then
      n
    else
      foo3 (h ())),
 translate_or_lose (foo3),
 foo3 (0));
10;

(kill (foo3), 0);
0;

/* The internal LOCLIST used by local should be empty right now */
?null (?loclist);
true;

/* The fpprintprec itself is not important in this test.  I'm
 * just picking something that has an ASSIGN property because
 * that's a separate internal case in the translator.
 *
 * This test is ugly, but it's testing different cases and
 * their interactions.
 */
block ([v],
  local (f1, f2, arr),
  f1 () := 0,
  f2 () := 123,
  arr [1] : "a",
  bar (fpprintprec) :=
    (local (f1, arr),
     fpprintprec : 5,
     f1 () := 42,
     arr [1] : "b",
     [block (
        local (f2, arr),
        f2 () := 69,
        arr [1] : "c",
        [f1 (), f2 (), arr [1]]),
      [f1 (), f2 (), arr [1]]]),
  translate_or_lose (bar),
  v : bar (3),
  [is (?get ('fpprintprec, '?assign) = false),
   v,
   [f1 (), f2 (), arr [1]]]);
[false,
 [[42, 69, "c"],
  [42, 123, "b"]],
 [0, 123, "a"]];

(kill (bar), 0);
0;

/* This is testing to make sure there are no bad interactions
 * between the usual local cleanup and errcatch cleanup (this
 * also mixes the interpreted and translated cases).  This test
 * is also ugly.
 *
 * The original implementation of local properties (from decades
 * ago) not only failed to clean up local properties at all, but
 * it wasn't even setting up the internal state to keep up with
 * these properties correctly.  An initial attempt at fixing bug
 * #2976 made this problem clear because with that it was easy to
 * cause an infinite loop during certain things like errcatch
 * cleanup.
 */
block ([translate : false,
        vi, vt],
  local (f3),
  f3 () := -10,
  baz1 () :=
    (error ("oops 1"),
     local (f4),
     f4 () := 0),
  baz2 () :=
    (local (f5),
     f5 () := 1,
     error ("oops 2")),
  translate_or_lose (baz1, baz2),
  baz_test () :=
    [block (
       local (f3),
       f3 () := -1,
       errcatch (baz1 ()),
       f3 ()),
     block (
       local (f3),
       f3 () := -2,
       errcatch (baz2 ()),
       f3 ())],
  vi : baz_test (),
  translate_or_lose (baz_test),
  vt : baz_test (),
  [vi,
   vt,
   is (f3 () = -10),
   is (f4 () = 0),
   is (f5 () = 1)]);
[[-1, -2],
 [-1, -2],
 true,
 false,
 false];

/* The internal LOCLIST used by local should be empty right now */
?null (?loclist);
true;

(kill (baz1, baz2, baz_test), 0);
0;

/***** This ends the bug #2976 tests *****/

/* compile wasn't always compiling the correct function
 *
 * This test not only depends on the internal details of how certain
 * functions are currently translated, but it also depends on internal
 * details about how DEFMFUN defines functions.  This also doesn't
 * really test that the correct function gets compiled because the
 * lisp implementation could have just compiled it itself anyway.  Ugh.
 */

(foo () := 1,
 compile_or_lose (foo),
 ?compiled\-function\-p (?symbol\-function (?get (foo, ?impl\-name))));
true;

(kill (foo), 0);
0;

/* Some internal function definitions and compiler macros were not
 * being cleaned up, and this could cause confusing and bogus results
 * when an outdated compiler macro was being used.
 *
 * Specifically one problem we had involved translating a function,
 * redefining it and then translating the new definition.  The internal
 * function and compiler macro from the original function could be used
 * when compiling calls to the new function if they were not overwritten.
 *
 * This all depended on lisp implementation-dependent behavior because
 * implementations are not required to ever use compiler macros.  Ugh.
 *
 * This test also depends on internal details of how certain functions
 * are currently translated.  Double ugh.
 */

(foo () := 0,
 translate_or_lose (foo),
 kill (foo),
 foo ([l]) := l,
 translate_or_lose (foo),
 test1 () := foo (),
 test2 () := foo (1, 2, 3),
 compile_or_lose (test1, test2),
 /* Previously we observed test1 returning 0 and test2 causing a lisp
  * error because the compiler macro and old internal function from
  * the first foo were being used.
  */
 [test1 (), test2 ()]);
[[], [1, 2, 3]];

(kill (foo, test1, test2), 0);
0;

/* https://stackoverflow.com/questions/64631208/compilation-global-variables-with-warning
 *
 * First verify that error_syms and niceindicespref assignments work as expected.
 */

kill (aa, bb, cc);
done;

errcatch (error_syms: 123);
[];

errcatch (error_syms: [aa, bb, 123]);
[];

error_syms: [aa, bb, cc];
[aa, bb, cc];

errcatch (niceindicespref: 123);
[];

errcatch (niceindicespref: []);
[];

niceindicespref: [aa, bb, cc];
[aa, bb, cc];

(reset (error_syms, niceindicespref), 0);
0;

/* now the example from the Stackoverflow question */

(program_content:
"define_variable(foo, true, boolean)$
foo: true$

exprp(that) := if foo = false and listp(that) and not emptyp(that) and member(that[1], [\"+\", \"*\"]) then(foo: true, true)$
matchdeclare(exprm, exprp)$
defrule(rule_1, exprm, subst(exprm[1], \"[\", exprm[2]))$

calc(list) := block([steps: []],
while foo do(
    steps: endcons(list, steps),
    foo: false,
    list: applyb1(list, rule_1)
),
steps
)$

calc_result: calc([\"+\", [[\"*\", [1, 2, 3]], [\"+\", [3, 4, 6]]]]);",
program_file_name: sconcat (maxima_tempdir, "/tmp_program.mac"),
with_stdout (program_file_name, print (program_content)),
0);
0;

kill (calc_result);
done;

([file_name_original, file_name_LISP, file_name_UNLISP, file_name_compiled]: compile_file (program_file_name), 0);
0;

stringp (file_name_compiled);
true;

calc_result;
calc_result;

(load (file_name_compiled),
 calc_result);
[["+", [["*", [1, 2, 3]], ["+", [3, 4, 6]]]],
 ["+", [6, ["+", [3, 4, 6]]]],
 ["+", [6, 13]],
 19];

(kill (program_content, program_file_name, file_name_original, file_name_LISP, file_name_UNLISP, file_name_compiled, calc_result), 0);
0;


/* Some additional basic tests for functions with rest args */

block ([translate : false],
  foo ([r]) := r,
  bar (a, b, [c]) := [a, b, c],
  test () :=
    [foo (),
     foo (1),
     foo (1, 2, 3),
     errcatch (bar ()),
     errcatch (bar (1)),
     bar (1, 2),
     bar (1, 2, 3),
     bar (1, 2, 3, 4, 5)],

  /* l1: foo, bar and test are interpreted */
  l1 : test (),

  /* l2: foo and bar are translated, and test is interpreted */
  translate_or_lose (foo, bar),
  l2 : test (),

  /* l3: foo, bar and test are translated */
  translate_or_lose (test),
  l3 : test (),

  [is (l1 = l2),
   is (l2 = l3),
   l1]);
[true,
 true,
 [[],
  [1],
  [1, 2, 3],
  [],
  [],
  [1, 2, []],
  [1, 2, [3]],
  [1, 2, [3, 4, 5]]]];

(kill (foo, bar, test, l1, l2, l3), 0);
0;

/* Attempting to translate a macro with a rest arg always caused an
 * error during translation because the translator was constructing
 * bogus Maclisp-style lexpr lambda expressions.
 */

block ([translate : false],
  foo ([r]) ::=
    buildq ([r], ['r, r]),
  bar (a, b, [c]) ::=
    buildq ([a, b, c], ['a, a, 'b, b, 'c, c]),
  test1 () :=
    block ([x : 1, z : 3],
      [foo (),
       foo (x),
       foo (x, y, z),
       bar (x, y),
       bar (x, y, z),
       bar (x, y, z, 4, 5, 6)]),
  /* test2 cannot be translated due to the WNA error during macro
   * expansion, but we can call and test it in the interpreter
   */
  test2 () :=
    [errcatch (bar ()),
     errcatch (bar (1))],

  /* l1: foo, bar and test1 are interpreted */
  l1 : test1 (),

  /* l2: foo and bar are translated, and test1 is interpreted */
  translate_or_lose (foo, bar),
  l2 : test1 (),

  /* l3: foo, bar and test1 are translated */
  translate_or_lose (test1),
  l3 : test1 (),

  [test2 (),
   is (l1 = l2),
   is (l2 = l3),
   l1]);
[[[], []],
 true,
 true,
 [[[], []],
  [['x], [1]],
  [['x, 'y, 'z], [1, 'y, 3]],
  ['x, 1, 'y, 'y, [], []],
  ['x, 1, 'y, 'y, ['z], [3]],
  ['x, 1, 'y, 'y, ['z, 4, 5, 6], [3, 4, 5, 6]]]];

(kill (foo, bar, test1, test2, l1, l2, l3), 0);
0;

/* Some additional basic tests for conditionals.
 *
 * We test both elseif and else-if ("else if").
 */

block ([translate : false],
  mysignum1 (x) := if x > 0 then 1 elseif  x < 0 then -1 else 0,
  mysignum2 (x) := if x > 0 then 1 else if x < 0 then -1 else 0,
  foo () :=
    [if true then 1,
     if false then 1,
     if true then 1 else 2,
     if false then 1 else 2,
     if 1 < 2 then 'y,
     if 1 < 2 then 'y else 'n,
     if 1 > 2 then 'n,
     if 1 > 2 then 'n else 'y,
     if 1 > 2 then 'n elseif  1 = 2 then 'n else 'y,
     if 1 > 2 then 'n else if 1 = 2 then 'n else 'y,
     mysignum1 (-3),
     mysignum2 (-3),
     mysignum1 (0),
     mysignum2 (0),
     mysignum1 (2),
     mysignum2 (2)],
  l1 : foo (),
  translate_or_lose (mysignum1, mysignum2, foo),
  l2 : foo (),
  [is (l1 = l2),
   l2]);
[true,
 [1, false, 1, 2, 'y, 'y, false, 'y, 'y, 'y, -1, -1, 0, 0, 1, 1]];

(kill (mysignum1, mysignum2, foo, l1, l2), 0);
0;

/* Bogus translations of nested conditionals in elseif clauses
 *
 * The translation of a conditional with another conditional nested
 * directly under an elseif clause was totally wrong.  Using else-if
 * ("else if") instead of elseif would work fine.
 *
 *
 * We use the with_both_elseifs macro so we can test both elseif and
 * else-if without having to duplicate portions of the tests below.
 * Give this macro a conditional expression with elseifs and it will
 * expand into a list: the first element is the same expression given
 * to it (with elseifs), and the second element is that same expression
 * rewritten to use else-ifs instead of elseifs.
 */

(to_else_if (expr) :=
   if mapatom (expr) then
     expr
   else
     block ([op : op (expr), args : args (expr)],
       if op = "if" and length (args) > 4 then
         funmake (op, map ('to_else_if, append (firstn (args, 2), [true, funmake (op, rest (args, 2))])))
       else
         funmake (op, map ('to_else_if, args))),
 with_both_elseifs (expr) ::=
   buildq ([expr, texpr : to_else_if (expr)],
     [expr, texpr]),
  0);
0;

block ([translate : false],
  foo () :=
    with_both_elseifs (
      if false then
        'lose1
      elseif false then
        'lose2
      elseif false then
        if true then
          'lose3
        else
          'lose4
      else
        'win),

  /* l1: foo is interpreted */
  l1 : foo (),

  translate_or_lose (foo),

  /* l2: foo is translated
   *
   * foo used to give lose3 instead of win in the elseif case.
   */
  l2 : foo (),

  [is (l1 = l2),
   l2]);
[true,
 ['win, 'win]];

block ([translate : false],
  /* There is nothing special about bar here.  This is just some
   * function that has several branches with nested conditionals.
   */
  bar (x) :=
    with_both_elseifs (
      if x > 5 then
        if x > 7 then
          'more_than_seven
        elseif x > 6 then
          'seven
        else
          'six
      elseif x > 2 then
        if x > 4 then
          'five
        elseif x > 3 then
          'four
        else
          'three
      elseif x >= 0 then
        if x > 1 then
          'two
        elseif x > 0 then
          'one
        else
          'zero
      else
        'negative),

  /* We test bar with the integers -2 to 9 */
  inputs : makelist (k, k, -2, 9),

  /* l1: bar is interpreted */
  l1 : map (bar, inputs),

  translate_or_lose (bar),

  /* l2: bar is translated
   *
   * bar used to give incorrect results in the elseif case for every
   * number less than or equal to 2 (which means we got incorrect
   * results for the integers -2 to 2 in this test).
   */
  l2 : map (bar, inputs),

  [is (l2 = l1),
   l2]);
[true,
 [['negative, 'negative],
  ['negative, 'negative],
  ['zero, 'zero],
  ['one, 'one],
  ['two, 'two],
  ['three, 'three],
  ['four, 'four],
  ['five, 'five],
  ['six, 'six],
  ['seven, 'seven],
  ['more_than_seven, 'more_than_seven],
  ['more_than_seven, 'more_than_seven]]];

(kill (foo, bar, l1, l2, inputs, to_else_if, with_both_elseifs), 0);
0;

/* Bogus translations of conditionals with tests that translated to T
 * and consequents that translated to NIL.
 */

block ([translate : false],
  foo () :=
    [if true then false else 1,
     if true then false elseif true then 1 else 2,
     if false then true elseif true then false else 1],

  /* l1: foo is interpreted */
  l1 : foo (),

  translate_or_lose (foo),

  /* l2: foo is translated
   *
   * foo used to return [1, 1, 1]
   */
  l2 : foo (),

  [is (l2 = l1),
   l2]);
[true,
 [false, false, false]];

(kill (foo, l1, l2), 0);
0;

/* Bug #3704: Translator gives internal error
 *
 * The hyper_to_summand function is from the bug report.
 */

(hyper_to_summand(e,k) := subst(hypergeometric = lambda([P,Q,x], 
    P : xreduce("*", map(lambda([zz], pochhammer(zz,k)),P)),
    Q : xreduce("*", map(lambda([zz], pochhammer(zz,k)),Q)),
    P*x^k/(k! * Q)),e),
 l1 : hyper_to_summand (hypergeometric ([1/2], [2/5], x), 2),
 translate_or_lose (hyper_to_summand),
 l2 : hyper_to_summand (hypergeometric ([1/2], [2/5], x), 2),
 [is (l1 = l2), l2]);
[true, 75 * x^2 / 112];

(foo () := lambda ([], x!),
 translate_or_lose (foo),
 block ([x : 5], foo () ()));
120;

(kill (hyper_to_summand, foo, l1, l2), 0);
0;

/* go tags can be integers
 *
 * This has been allowed, but it used to give a warning and an extra
 * trivial run through the translator to translate the integer go tags.
 * Now we allow integers directly without giving a warning.
 *
 * We don't actually bother to check for warnings in the test below.
 * We're really just verifying that using an integer go tag works.
 */

block ([translate : false],
  foo () := block ([i : 0], tag, i : i + 1, if i < 5 then go (tag), i),
  bar () := block ([i : 0], 123, i : i + 1, if i < 5 then go (123), i),
  l1 : [foo (), bar ()],
  translate_or_lose (foo, bar),
  l2 : [foo (), bar ()],
  [is (l1 = l2), l2]);
[true, [5, 5]];

(kill (foo, bar, l1, l2), 0);
0;

/* A bug in MARRAYREF caused things like translated array references
 * to yield MQAPPLY expressions with an incorrect header.
 */

block ([translate : false],
  foo () := 'baz () [1],
  bar () := 'baz () [1, 2, 3],
  l1 : [foo (), bar ()],
  translate_or_lose (foo, bar),
  l2 : [foo (), bar ()],
  [is (l1 = l2), l2]);
[true, ['baz () [1], 'baz () [1, 2, 3]]];

(kill (foo, bar, l1, l2), 0);
0;

/* A bug in MARRAYREF caused bogus indexing into hash tables and fast
 * arrays.  This affected things like translated array references.
 */

block ([translate : false,
        use_fast_arrays : true],

  foo () := block ([a],
              a[false] : 'wtf,
              a[1] : 2,
              a[1]),

  /* This would correctly yield 2 */
  l1 : foo (),

  translate_or_lose (foo),

  /* This used to incorrectly yield wtf */
  l2 : foo (),

  [is (l1 = l2), l2]);
[true, 2];

(kill (foo, l1, l2), 0);
0;

/* A bug in MARRAYREF caused things like translated array references
 * to yield expressions with an incorrect header.
 */

block ([translate : false],
  foo () := block ([a],
              local (a),
              array (a, complete, 5),
              a[3]),

  /* This would correctly yield a[3] */
  l1 : foo(),

  translate_or_lose (foo),

  /* This would incorrectly yield a(3) */
  l2 : foo(),

  [is (l1 = l2), l2]);
[true, 'a[3]];

(kill (foo, l1, l2), 0);
0;

/* When translate_fast_arrays:true, a lisp error would occur at runtime
 * during an attempted MQAPPLY array assignment
 */

block ([translate : false],
  foo () := block ([a],
              local (a, b),
              a : make_array ('fixnum, 5),
              b () := a,
              b () [3] : 17,
              b () [3]),

  /* This would correctly yield 17 */
  l1 : foo(),

  block ([translate_fast_arrays : false],
    translate_or_lose (foo)),

  /* This would correctly yield 17 */
  l2 : foo(),

  block ([translate_fast_arrays : true],
    translate_or_lose (foo)),

  /* This would cause a lisp error */
  l3 : foo(),

  [is (l1 = l2), is (l2 = l3), l3]);
[true, true, 17];

(kill (foo, l1, l2, l3), 0);
0;

/* The string "**" no longer translates to the string "^".
 * This test compares the interpreted and translated results.
 */

block ([translate : false],
  foo () := ["^", "^" (2, 3), apply ("^", [2, 3]),
             "**", "**" (2, 3), apply ("**", [2, 3])],
  l1 : foo (),
  translate_or_lose (foo),
  l2 : foo (),
  [l2, is (l1 = l2)]);
[["^", 8, 8, "**", 8, 8], true];

(kill (foo, l1, l2), 0);
0;

/* Attempting to translate some atoms like lisp arrays would
 * cause lisp errors during translation.
 */

(a : make_array (fixnum, 1),
 a[0] : 13,
 define (foo (), a),
 translate_or_lose (foo),
 listarray (foo ()));
[13];

(kill (foo, a), 0);
0;

/* Simple tests for catch and throw */

block ([translate : false, l1, l2],
  local (foo, bar, baz),

  foo (p) := if p then throw (13) else 2,
  bar () := catch (1, foo (false), 3),
  baz () := catch (1, foo (true), 3),

  l1 : [bar (), baz ()],

  translate_or_lose (foo, bar, baz),

  l2 : [bar (), baz ()],

  [l2, is (l1 = l2)]);
[[3, 13], true];

/* Translating a define_variable form with translate (but not
 * translate_file or compfile) used to invoke undefined behavior.
 * This would cause a lisp error during translation under some
 * (but not all) lisp implementations.
 */

block ([translate : false],
  local (foo),
  foo () := (define_variable (x, 1, fixnum), x),
  translate_or_lose (foo),
  foo ());
1;

(kill (foo, x), 0);
0;

/* If local was used on a matchdeclared pattern variable, and this
 * was all translated with something besides translate_file (e.g.,
 * translate, compfile, etc.), then the MATCHDECLARE property would
 * not be on the pattern variable.
 */

block ([translate : false, l1, l2],
  local (foo),

  foo () := (local (x), matchdeclare (x, true), let (a * x, x), letsimp (a * q)),

  /* This would yield q */
  l1 : foo (),

  translate_or_lose (foo),

  /* This used to yield a*q */
  l2 : foo (),

  [l2, is (l1 = l2)]);
[q, true];

(kill (foo), 0);
0;

/* Rest args are now allowed in lambda expressions in MQAPPLY
 * lambda forms
 */

block ([translate : false, l1, l2],
  local (foo, bar, baz),

  /* foo used to fail to translate due to the rest arg */
  foo () :=
    block ([x : 1, z : 3],
      lambda ([[x]], x) (x, x + 1, z)),
  bar () :=
    block ([x : 2, z : 4],
      apply (lambda ([[x]], x), [x, x + 1, z])),
  baz () :=
    block ([x : 3, z : 5],
      block ([f : lambda ([[x]], x)],
        f (x, x + 1, z))),

  l1 : [foo (), bar (), baz ()],

  translate_or_lose (foo, bar, baz),

  l2 : [foo (), bar (), baz ()],

  [l1, is (l1 = l2)]);
[[[1, 2, 3],[2, 3, 4],[3, 4, 5]], true];

/* Validation has been improved for lambda expressions in MQAPPLY
 * lambda forms
 */

block ([translate : false],
  local (foo, bar),

  /* These should both fail to translate */
  foo () := lambda ([]) (),
  bar () := lambda ([x, x], x) (1, 2),

  translate (foo, bar));
[];

/* The translation of array functions was broken for decades */

block ([translate : false, l1, l2],
  local (foo, bar),

  foo[x] := x,
  bar[n] := if n = 1 then 1 else n * bar[n - 1],

  l1 : [foo[0], foo[5], bar[5], bar[10]],

  translate_or_lose (foo, bar),

  l2 : [foo[0], foo[5], bar[5], bar[10]],

  [l1, is (l1 = l2)]);
[[0, 5, 120, 3628800], true];

(kill (foo, bar), 0);
0;

/* The translation of upward funargs (including those created by
 * subscripted functions) easily lead to lisp errors.
 */

/* Tests involving returned lambdas without free vars that were
 * bound during definition
 */
block ([l1, l2,
        translate : false,
        listarith : true],
  local (foo, bar, test),

  foo () := lambda ([x], 2 * x + q),
  bar () := lambda ([x, [y]], x * y + q),

  test () :=
    block ([f : foo (),
            b : bar ()],
      [f (3), f (5), b (2, 3, 4), b (5, 6, 7)]),

  l1 : test (),

  translate_or_lose (foo, bar),

  l2 : test (),

  [l2, is (l1 = l2)]);
[['q + 6, 'q + 10, ['q + 6, 'q + 8], ['q + 30, 'q + 35]],
 true];

(kill (foo, bar), 0);
0;

/* Tests involving returned lambdas with free vars that were
 * bound during definition.  These do not cause the capture of
 * values.
 */
block ([l1, l2,
        x : 'ux,
        translate : false,
        listarith : true],
  local (foo, bar, baz, test),

  foo (x) := lambda ([y], x + y + q),
  bar (x) := lambda ([y, [z]], q + x + y * z),
  baz (v) := lambda ([], v),

  test () :=
    block ([f : foo (3),
            b : bar (4),
            c : baz (5)],
      [f (5), b (2, 3, 4), c ()]),

  l1 : test (),

  translate_or_lose (foo, bar, baz),

  l2 : test (),

  [l2, is (l1 = l2)]);
[['q + 'ux + 5,
  ['q + 'ux + 6, 'q + 'ux + 8],
  'v],
 true];

(kill (foo, bar, baz), 0);
0;

/* Tests involving subscripted functions.  These do cause the capture
 * of values.
 */
block ([l1, l2,
        x : 'ux, y : 'uy,
        translate : false],
  local (foo, bar, baz, def, test),

  def () := (
    foo[x, y](a, b) := [x, y, a, b, q],
    bar[x, y](a, [b]) := [x, y, a, b, q],
    baz[v]() := v),

  test () :=
    block ([f : foo[1, 2],
            b : bar[3, 4],
            c : baz[5]],
      [f (6, 7), b (8, 9, 10), c ()]),

  def (),

  l1 : test (),

  /* just kill and redefine */

  kill (foo, bar, baz),

  def (),

  translate_or_lose (foo, bar, baz),

  l2 : test (),

  [l2, is (l1 = l2)]);
[[[1, 2, 6, 7, 'q],
  [3, 4, 8, [9, 10], 'q],
  5],
 true];

(kill (foo, bar, baz), 0);
0;

/* More tests involving multiple nested lambdas */
block ([l1, l2,
        x : 'ux, y : 'uy, z : 'uz,
        translate : false],
  local (foo, bar, baz, quux, def, test),

  def () := (
    /* nothing should be captured */
    foo (x) := lambda ([y], lambda ([z], [x, y, z])),
    /* x should be captured and used */
    bar[x](y) := lambda ([z], [x, y, z]),
    /* x should be captured and used */
    baz[x](y) := lambda ([z], lambda ([], [x, y, z])),
    /* nothing should be captured since x is bound by the inner lambda */
    quux[x](y) := lambda ([x], [x, y])),

  test () :=
    block ([a : foo (1),
            b : bar[2],
            c : baz[3],
            d : quux[4]],
      [a (10) (11), b (12) (13), c (14) (15) (), d (16) (17)]),

  def (),

  l1 : test (),

  /* just kill and redefine */

  kill (foo, bar, baz, quux),

  def (),

  translate_or_lose (foo, bar, baz, quux),

  l2 : test (),

  [l2, is (l1 = l2)]);
[[['ux, 'uy, 11],
  [2, 'uy, 13],
  [3, 'uy, 'uz],
  [17, 'uy]],
 true];

(kill (foo, bar, baz, quux), 0);
0;





/*** KILLING THESE FUNCTIONS SHOULD BE THE LAST TEST IN THIS FILE ***/
(kill (translate_or_lose, compile_or_lose), 0);
0;
/*** THERE SHOULD BE NO TESTS BEYOND THIS POINT ***/