Fix acos (-1) in round-downwards mode on x86 (bug 14034)

[Andreas Jaeger]

On 04/29/2012 05:01 PM, Joseph S. Myers wrote:
> Bug 14034 is the problem that acos (-1) returns -pi instead of pi in
> round-downwards mode, for x86 for all floating-point formats and for
> x86_64 for long double (x86_64 #includes the x86 implementation of
> acosl).  The ISO C requirement is that the result is always in the
> range [0, pi].
>
> The problem is that the fsqrt instruction follows the IEEE 754
> requirement that sqrt(-0) is -0, and a previous subtraction resulted
> in -0 (x-x is -0 in round-downwards mode), so the fpatan instruction
> gets a -0 value where it needs a value without the sign bit set to
> produce results in the correct quadrant.  I propose this patch fixing
> this in the obvious way by taking the absolute values of the square
> roots.  I've added tests for acos in all rounding modes - and for asin
> although the similar square roots there do not cause any problems.
>
> Tested x86 and x86_64 and ulps updated accordingly.
>
> 2012-04-29  Joseph Myers<joseph@codesourcery.com>
>
> 	[BZ #14034]
> 	* sysdeps/i386/fpu/e_acos.S (__ieee754_acos): Take absolute value
> 	of square root.
> 	* sysdeps/i386/fpu/e_acosf.S (__ieee754_acosf): Likewise.
> 	* sysdeps/i386/fpu/e_acosl.c (__ieee754_acosl): Likewise.
> 	* math/libm-test.inc (acos_test_tonearest): New function.
> 	(acos_test_towardzero): Likewise.
> 	(acos_test_downward): Likewise.
> 	(acos_test_upward): Likewise.
> 	(asin_test_tonearest): Likewise.
> 	(asin_test_towardzero): Likewise.
> 	(asin_test_downward): Likewise.
> 	(asin_test_upward): Likewise.
> 	(main): Call the new functions.
> 	* sysdeps/i386/fpu/libm-test-ulps: Update.
> 	* sysdeps/x86_64/fpu/libm-test-ulps: Update.

thanks, this is ok.

Andreas

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