The fixes look good on their face, and solve the immediate problem, but may cause other problems. Indeed, until we know what
float:t, numer:t, float(), etc. are supposed to do, it is hard to say whether they are correct. The second fix in particular
immediately causes problems (see below).
To see what they currently do (which I'd hope has some vague relationship to what they're supposed to do), I put together a little
test (below). This test shows many peculiarities. One of them is, I believe, intentional (though perhaps questionable):
a.. Only numer:t and float:t go inside of an array subscript to evaluate numerically
But most of them appear to be bugs:
a.. numer:t evaluates %e^(3/2), but not %e
b.. numer:t is the only case which treats %e and %pi differently
c.. float:t doesn't evaluate sin(2), but does evaluate exp(3/2); float() does the opposite.
d.. bfloat:t acts exactly like bfloat(), unlike float:t vs. float()
e.. float() and bfloat() don't agree in many cases
f.. numer:t evaluates one expt but not the other in 3^%e/2^%e
g.. why on earth does bfloat:t change fix to entier?
h.. etc.
But let's not throw out the baby with the bathwater. The purpose of all the complexity around %e is to prevent strictly symbolic
expressions from becoming gratuitously numerical; who wants to see exp(%i*x) => 2.718^(%i*x)? This currently never happens; neither
does x^3 => x^3.0 or 1/x => x^-1.0. On the other hand, sin(%pi*x) does gratuitously become sin(3.142*x), except in float(). Some
functions preserve 5^x and x^(1/3), others don't. For real fun, try flotest((-1)^float(1/3)) -- though part of that is really a
different issue....
-S
--------------------------------------------------------------------------------
tests: [%E,%PI,2^(3/4),SIN(2),%E^(3/2),3^%E/2^%E, SIN(2)^%PI,a[FIX(SQRT(5))] ];
flotest(r) := [EV(r, NUMER), EV(r, FLOAT), EV(r, FLOAT, NUMER), EV(r, BFLOAT), FLOAT(r),
BFLOAT(r)];
fpprec:4;
apply(matrix,flotest(tests));
%E
3/4 3/2 3 %PI %E %PI 2 SIN(2) %E --- SIN
(2) a %E FIX(SQRT(5))
2
[ %E ]numer [ %E 3.142 1.682
0.91 4.482 0.15 3 0.74 a ]
[ 2 ]
[ ]
[ %E ]
[ 3 %PI ]float [ %E %PI 1.682
SIN(2) 4.482 --- SIN (2) a ] [ %E
2 ] [ 2 ]
[ ]
[ %E ]float, [ %E 3.142 1.682
0.91 4.482 0.15 3 0.74 a ]numer
[ 2 ]
[ ]bfloat [ 2.718B0 3.142B0 1.682B0
9.093B-1 4.482B0 3.011B0 7.418B-1 a ]
[ ENTIER(SQRT(5)) ]
[ ]
[ %E ]
[ 3/2 3.0 %PI ]float() [ %E %PI 1.682
0.91 %E ----- 0.91 a ] [ %E
FIX(SQRT(5)) ] [ 2.0 ]
[ ]bfloat() [ 2.718B0 3.142B0 1.682B0
9.093B-1 4.482B0 3.011B0 7.418B-1 a ]
[ FIX(SQRT(5)) ]
PS As far as I can tell, there is no reasonable way to evaluate subscripts as bfloats; even scanmap does not go into subscripts.
But I doubt that cases like a[fix(10 * (100000000000000000000 * sqrt(2) - 141421356237309504880))] come up in real life very
often....