## digitalmars.D - Re: Semantics of ^^

Jason House <jason.james.house gmail.com> writes:
```I think you have a bad corner case:

enum int ct = -1;
immutable rt = -1;

ct ^^ ct // Error (compile time)
rt ^^ ct // Error (compile time)
rt ^^ rt // Error (run time)
ct ^^ rt // Works??? (after rewrite)

Don Wrote:

Based on everyone's comments, this is what I have come up with:

--------------------
x ^^ y is right associative, and has a precedence intermediate between
multiplication and unary operators.

* The type of x ^^ y is the same as the type of x * y.
* If y == 0,  x ^^ y is 1.
* If both x and y are integers, and y > 0,  x^^y is equivalent to
{ auto u = x; foreach(i; 1..y) { u *= x; } return u; }
* If both x and y are integers, and y < 0, an integer divide error
occurs, regardless of the value of x. This error is detected at compile
time, if possible.
* If either x or y are floating-point, the result is pow(x, y).
--------------------
Rationale:
(1) Although the following special cases could be defined...
* If x == 1,  x ^^ y is 1
* If x == -1 and y is even, x^^y == 1
* If x == -1 and y is odd, x^^y == -1
... they are not sufficiently useful to justify the major increase in
complexity which they introduce. In all other cases, a negative exponent
indicates an error; it should be rewritten as (cast(real)x) ^^ y. Making
these cases errors makes everything much simpler, and allows the
compiler to use range propagation on the value of y to detect most
exponentiation errors at compile time. (If those cases are legal, the
compiler can't generate an error on x^^-2, because of the possibility
that x might be 1 or -1).
Also note that making it an error leaves open the possibility of
changing it to a non-error later, without breaking code; but going from
non-error to error would be more difficult.

(2) USE OF THE INTEGER DIVIDE ERROR
Note that on x86 at least, a hardware "integer divide error", although
commonly referred to as "division by zero", also occurs when the DIV
instruction, which performs uint = ulong/uint, results in a value
greater than uint.max. Raising a number to a negative power does involve
a division, so it seems to me not unreasonable to use it for this case
as well.
Note that 0 ^^ -1 is a division by zero.
This means that, just as you should check that y!=0 before performing
x/y, you should check that y>=0 before performing x^^y.

(3) OVERFLOW
int ^^ int returns an int, not a long. Although a long would allow
representation of larger numbers, even doubling the number of bits
doesn't help much in avoiding overflow, because x^^y is exponential.
Even a floating-point representation can easily overflow:
5000^5000 easily overflows an 80-bit real.
So, it's preferable to retain the simplicity that typeof(x^^y) is
typeof(x*y).

```
Dec 09 2009
Jason House <jason.james.house gmail.com> writes:
```oops, my message was supposed to be in reply to version 3 that included the
rewrite rule for -1 ^^ y

Jason House Wrote:

I think you have a bad corner case:

enum int ct = -1;
immutable rt = -1;

ct ^^ ct // Error (compile time)
rt ^^ ct // Error (compile time)
rt ^^ rt // Error (run time)
ct ^^ rt // Works??? (after rewrite)

Don Wrote:

Based on everyone's comments, this is what I have come up with:

--------------------
x ^^ y is right associative, and has a precedence intermediate between
multiplication and unary operators.

* The type of x ^^ y is the same as the type of x * y.
* If y == 0,  x ^^ y is 1.
* If both x and y are integers, and y > 0,  x^^y is equivalent to
{ auto u = x; foreach(i; 1..y) { u *= x; } return u; }
* If both x and y are integers, and y < 0, an integer divide error
occurs, regardless of the value of x. This error is detected at compile
time, if possible.
* If either x or y are floating-point, the result is pow(x, y).
--------------------
Rationale:
(1) Although the following special cases could be defined...
* If x == 1,  x ^^ y is 1
* If x == -1 and y is even, x^^y == 1
* If x == -1 and y is odd, x^^y == -1
... they are not sufficiently useful to justify the major increase in
complexity which they introduce. In all other cases, a negative exponent
indicates an error; it should be rewritten as (cast(real)x) ^^ y. Making
these cases errors makes everything much simpler, and allows the
compiler to use range propagation on the value of y to detect most
exponentiation errors at compile time. (If those cases are legal, the
compiler can't generate an error on x^^-2, because of the possibility
that x might be 1 or -1).
Also note that making it an error leaves open the possibility of
changing it to a non-error later, without breaking code; but going from
non-error to error would be more difficult.

(2) USE OF THE INTEGER DIVIDE ERROR
Note that on x86 at least, a hardware "integer divide error", although
commonly referred to as "division by zero", also occurs when the DIV
instruction, which performs uint = ulong/uint, results in a value
greater than uint.max. Raising a number to a negative power does involve
a division, so it seems to me not unreasonable to use it for this case
as well.
Note that 0 ^^ -1 is a division by zero.
This means that, just as you should check that y!=0 before performing
x/y, you should check that y>=0 before performing x^^y.

(3) OVERFLOW
int ^^ int returns an int, not a long. Although a long would allow
representation of larger numbers, even doubling the number of bits
doesn't help much in avoiding overflow, because x^^y is exponential.
Even a floating-point representation can easily overflow:
5000^5000 easily overflows an 80-bit real.
So, it's preferable to retain the simplicity that typeof(x^^y) is
typeof(x*y).

```
Dec 09 2009
Don <nospam nospam.com> writes:
```Jason House wrote:
I think you have a bad corner case:

enum int ct = -1;
immutable rt = -1;

ct ^^ ct // Error (compile time)
rt ^^ ct // Error (compile time)
rt ^^ rt // Error (run time)
ct ^^ rt // Works??? (after rewrite)

No, they will all work. Both rt and ct are manifest constants.
```
Dec 09 2009
Don <nospam nospam.com> writes:
```Don wrote:
Jason House wrote:
I think you have a bad corner case:

enum int ct = -1;
immutable rt = -1;

ct ^^ ct // Error (compile time)

rt ^^ ct // Error (compile time)
rt ^^ rt // Error (run time)
ct ^^ rt // Works??? (after rewrite)

No, they will all work. Both rt and ct are manifest constants.

(Actually it's a bit of wierd compiler quirk that const/immutables
initialized with literal values are manifest constants; they aren't
constants if initialized with anything else. This behaviour may change,
but it doesn't affect this scheme).

If however rt is just

int rt = -1;

then

ct ^^ ct and ct ^^ rt work, and the other two fail. This is intended.
```
Dec 09 2009