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Re: floor, ceil, trunc, round, minus zero, and alpha

From: Eric Blake
Subject: Re: floor, ceil, trunc, round, minus zero, and alpha
Date: Mon, 20 Dec 2010 14:08:08 -0700
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On 12/20/2010 08:44 AM, Bruno Haible wrote:
> Eric Blake wrote:
>>>   - are marked as [MX] in POSIX [1][2][3][4], that is, an optional feature
>>>     not contained in ISO C 99,
>> [MX] means that the behavior is required on platforms that claim IEC
>> 60559 conformance (aka IEEE 754 format); it means that you fully
>> implement the otherwise-optional Appendix F of the C99 standard.
> I see. Thanks for correcting me.
> Regarding DEC Alpha platforms, I don't think they are 100% IEEE 754 + 854
> compliant, because the hardware designers took some shortcuts regarding
> the exception handling, in order to implement the floating-point operations
> in a single CPU cycle.
>>>   - make little sense for 'ceil' from a mathematical point of view:
>>>     ceil is a monotonically increasing function but POSIX wants
>>>     ceil(-0.5) = 0.0 and ceil(-0.0) = -0.0,
>> I'll raise that point with the Austin group.
> Given that the annex section F.9.6.1 in ISO C99 already specifies this
> behaviour, I don't think the Austin group will deviate from that.

Fred Tydeman pointed out that since POSIX [MX] shading defers to C99
Appendix F, which defers to IEEE 754, and IEEE 754 section 6.3 The Sign
Bit states:

... and the sign of the result of the round floating-point number to
integral value operation is the sign of the operand. These rules shall
apply even when operands or results are zero or infinite.

Therefore, POSIX requires ceil(-0.5) to return -0.0 when you are
strictly compliant (if you actually tested a system where it returns
+0.0, you found a bug, but the bug is only worth fixing if we care about

And indeed, glibc gives ieee-compliant behavior:

$ cat foo.c
#include <math.h>
#include <stdio.h>
int main (void)
  printf ("%d %d\n", signbit(ceil(-0.5)), signbit(ceil(0.5)));
  return 0;
$ gcc -o foo -Wall -g foo.c -lm
$ ./foo
128 0

Eric Blake   address@hidden    +1-801-349-2682
Libvirt virtualization library http://libvirt.org

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