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Floating-point arithmetic is quite different from the
arithmetic on integers or the one of real numbers.
In particular, most transformations, simplifications that can
be done on integers are invalid when done on floats.
For example:
- associativity doesn't hold
- distributivity doesn't hold
- comparison is tricky & complex
This is because (among others things):
- limited precision, rounding everywhere
- presence of signed zeroes
- presence of infinities
- presence of NaNs (signaling or quiet)
- presence of numbers without inverse
- several kind of exceptions.
Since they don't follow the same rules as their integer
counterpart, better to give them a specific opcode
instead of having to test the type of the operands at
each manipulation.
Signed-off-by: Luc Van Oostenryck <luc.vanoostenryck@gmail.com>
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Comparision of floating-point values can't be done
like for integral values because of the possibility to have
NaNs which can't be ordered with normal values or even between
themselves.
The real difference appears once there is any "reasoning"
done with the result of the comparison. For example, once NaNs
are taken in account: "!(a < b)" and "(a >= b)" are not the same.
In fact the usual comparison operators must be reinterpreted
as implicitely first testing if any of the operand is a Nan
and return 'false' if it is the case. Thus "a < b" becomes
"!isnan(a) && !isnan(b) && (a < b)".
If we need to negate the comparison we get "!(a < b)" which
naturally becomes "isnan(a) || isnan(b) || (a >= b)".
We thus need two sets of operators for comparison of floats:
one for the "ordered" values (only true if neither operand
is a Nan) and one for the "values" (also true if either
operand is a NaN). A negation of the comparison switch from one
of the set to the other.
So, introduce another set of instructions for the comparison
of floats.
Note: the C standard requires that:
*) "x == x" is false if x is a NaN,
*) "x != x" is true if x is a NaN,
and this is coherent with "x != x" <-> "!(x == x)".
Signed-off-by: Luc Van Oostenryck <luc.vanoostenryck@gmail.com>
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Currently only commutative instructions are canonicalized
(the "simpler" operands, often a constant, is forced, if present
to be in the second operand). This improve CSE (more cases are
considered as equivalent) and help to reduce the number of "pattern"
to be handled at simplification.
Do this also for compare instructions since in thsi case we can
swap the order of the operands if at the same time we also swap
the 'direction' on the comparison.
Signed-off-by: Luc Van Oostenryck <luc.vanoostenryck@gmail.com>
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Some optimizations transform an instruction opcode
into another. For example, it may be needed to know
the opcode corresponding to the negation of a comparison.
This patch make this easy and flexible by adding a table
for the relation between opcodes.
Signed-off-by: Luc Van Oostenryck <luc.vanoostenryck@gmail.com>
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