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libspl sys/sysmacros.h: Fix P2ROUNDUP_TYPED to not trigger integer overflow #3949
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After talking with @perfinion about this, I am confident that this is mathematically equivalent and can prove it. Here are axioms: a. (-(x)) === ( Here is a proof:
Then if we just clean up the unnecessarily parenthesis, we arrive at @perfinion's code. @behlendorf This looks good to me, provided the commit message includes the proof. |
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The original P2ROUNDUP and P2ROUNDUP_TYPED macros contain -x which triggers PaX's integer overflow detection for unsigned integers. Replace the macros with an equivalent version that does not trigger the overflow. Axioms: A. (-(x)) === (~((x) - 1)) === (~(x) + 1) under two's complement. B. ~(x & y) === ((~(x)) | (~(y))) under De Morgan's law. C. ~(~x) === x under the law of excluded middle. Proof: 0. (-(-(x) & -(align))) original 1. (~(-(x) & -(align)) + 1) by A 2. (((~(-(x))) | (~(-(align)))) + 1) by B 3. (((~(~((x) - 1))) | (~(~((align) - 1)))) + 1) by A 4. (((((x) - 1)) | (((align) - 1))) + 1) by C Q.E.D. Signed-off-by: Jason Zaman <[email protected]> Reviewed-by: Chris Dunlop <[email protected]> Reviewed-by: Richard Yao <[email protected]>
The original P2ROUNDUP and P2ROUNDUP_TYPED macros contain -x which triggers PaX's integer overflow detection for unsigned integers. Replace the macros with an equivalent version that does not trigger the overflow. Axioms: A. (-(x)) === (~((x) - 1)) === (~(x) + 1) under two's complement. B. ~(x & y) === ((~(x)) | (~(y))) under De Morgan's law. C. ~(~x) === x under the law of excluded middle. Proof: 0. (-(-(x) & -(align))) original 1. (~(-(x) & -(align)) + 1) by A 2. (((~(-(x))) | (~(-(align)))) + 1) by B 3. (((~(~((x) - 1))) | (~(~((align) - 1)))) + 1) by A 4. (((((x) - 1)) | (((align) - 1))) + 1) by C Q.E.D. Signed-off-by: Jason Zaman <[email protected]> Reviewed-by: Chris Dunlop <[email protected]> Reviewed-by: Richard Yao <[email protected]> Signed-off-by: Brian Behlendorf <[email protected]> Closes openzfs#3949
The original P2ROUNDUP and P2ROUNDUP_TYPED macros contain -x which triggers PaX's integer overflow detection for unsigned integers. Replace the macros with an equivalent version that does not trigger the overflow. Axioms: A. (-(x)) === (~((x) - 1)) === (~(x) + 1) under two's complement. B. ~(x & y) === ((~(x)) | (~(y))) under De Morgan's law. C. ~(~x) === x under the law of excluded middle. Proof: 0. (-(-(x) & -(align))) original 1. (~(-(x) & -(align)) + 1) by A 2. (((~(-(x))) | (~(-(align)))) + 1) by B 3. (((~(~((x) - 1))) | (~(~((align) - 1)))) + 1) by A 4. (((((x) - 1)) | (((align) - 1))) + 1) by C Q.E.D. Signed-off-by: Jason Zaman <[email protected]> Reviewed-by: Chris Dunlop <[email protected]> Reviewed-by: Richard Yao <[email protected]> Signed-off-by: Brian Behlendorf <[email protected]> Closes openzfs#3949
The original P2ROUNDUP and P2ROUNDUP_TYPED macros contain -x which triggers PaX's integer overflow detection for unsigned integers. Replace the macros with an equivalent version that does not trigger the overflow. Axioms: A. (-(x)) === (~((x) - 1)) === (~(x) + 1) under two's complement. B. ~(x & y) === ((~(x)) | (~(y))) under De Morgan's law. C. ~(~x) === x under the law of excluded middle. Proof: 0. (-(-(x) & -(align))) original 1. (~(-(x) & -(align)) + 1) by A 2. (((~(-(x))) | (~(-(align)))) + 1) by B 3. (((~(~((x) - 1))) | (~(~((align) - 1)))) + 1) by A 4. (((((x) - 1)) | (((align) - 1))) + 1) by C Q.E.D. Signed-off-by: Jason Zaman <[email protected]> Reviewed-by: Chris Dunlop <[email protected]> Reviewed-by: Richard Yao <[email protected]> Signed-off-by: Brian Behlendorf <[email protected]> Closes #3949
The original P2ROUNDUP and P2ROUNDUP_TYPED macros contain -x which triggers PaX's integer overflow detection for unsigned integers. Replace the macros with an equivalent version that does not trigger the overflow. Axioms: A. (-(x)) === (~((x) - 1)) === (~(x) + 1) under two's complement. B. ~(x & y) === ((~(x)) | (~(y))) under De Morgan's law. C. ~(~x) === x under the law of excluded middle. Proof: 0. (-(-(x) & -(align))) original 1. (~(-(x) & -(align)) + 1) by A 2. (((~(-(x))) | (~(-(align)))) + 1) by B 3. (((~(~((x) - 1))) | (~(~((align) - 1)))) + 1) by A 4. (((((x) - 1)) | (((align) - 1))) + 1) by C Q.E.D. Signed-off-by: Jason Zaman <[email protected]> Reviewed-by: Chris Dunlop <[email protected]> Reviewed-by: Richard Yao <[email protected]> Signed-off-by: Brian Behlendorf <[email protected]> Closes openzfs#3949
The original P2ROUNDUP_TYPED macro contains a -x which triggers PaX's
integer overflow detection for unsigned integers. Replace the macro with
an equivalent version that does not trigger the overflow.
Signed-off-by: Jason Zaman [email protected]
fixes #2505